Dad (93) was living alone, but had an accident and needed hip surgery. How do I know if he can still live on his own?

If it’s been 90 days and your dad still needs your help then ‘probably not’ on your question of can he live alone.
Where is he now? In his home? Are you in your home down the street or living with him? How is he on his ADLs? Does he need things a housekeeper could help with? Did he have home health when he came out of rehab? Did he continue his therapy at home? It’s difficult to give you an opinion without knowing more about his condition. Is your job in PA or NJ?
On the surface it would seem he needs to be in an ALF but it really all depends on why he still needs help 90 days after the fall that would prevent you from working. If you need to work and he needs help, then he has to change his residence or hire help. Try not to make it more complicated than that for him or you.

Based on his age alone, let alone an injury involved I would say that he needs assistance.

My mom broke hip at age 90 and went through rehab in a nursing home. After being released, she insisted that she wished to live in her own home (my husband and I live 4 minutes away). Mom was very sharp mentally, so we had no fears in that regard. She continued rehab at home, until she was stronger. Mom agreed to let us install a camera to keep an eye on her, and we installed the NEST indoor camera in her living room. Initially, I installed the cameras out of a sense of fear, however it gave me peace of mind when she didn't answer the phone, as I could but I see she if she was in the kitchen or bathroom, as I could see if the light was on from the hallway. She and I had the security that I could watch her from my computer (while working) or from my phone, if traveling. I also knew when she got up in the morning, as I could hear the television or see her. No more waking her up to check on her. Maintaining her quality of life was key to her recovery. At 93, she fractured her hip, while hurrying to the bathroom. We were able to get to her quickly, as we heard her groaning on the camera - she fell in the bathroom. Mom did not recover well from the second fall, and we lost her about a year later. It should be noted that being in the same home with your parent, does not guarantee that they won't fall. I was in the upstairs kitchen and Mom was going downstairs to the basement, when she missed the last step and broke her hip the first time. If your dad is mentally sound and can get around to take care of himself, without help, he is in a better position to let you know his wishes. Good luck to you and your family.

Breaking a hip is very serious in the elderly. At your Dad's age very much so. Bones get brittle with age and harder and longer to heal. I would say an evaluation while in rehab will help you make that decision.

Is he in rehab? The facility will monitor him to determine if he can live alone or if he will need a higher level of care.

I was going to ask whether the accident caused the broken hip, or the broken hip led to the accident - then on your profile I see your father has been diagnosed (?) with osteoporosis. Oh dear. The point is that anyone at any age can trip over the cat or slip on cooking oil, and then the broken hip is just an accident; but with osteoporosis falls and fractures become almost inevitable.

This doesn't on its own mean he can't live alone, but it does mean he'll be at serious risk of falling. What does he want to do?

I read in your profile that your father has osteoporosis.    Depending on the severity, it may affect his ability to stand strait, and that could shift the balance of his body as he walks.   That should be a consideration for future planning.

How did the accident occur?  Was it at home or elsewhere?   That also could make a difference in his future planning.

Pblise offers good suggestions for remediation actions.    There are others that can be taken.   Since your father's at home, I assume he received home PT including from OT as well as nursing?   In my experience, they offer excellent insight into factors contributing to falls, even if some of them aren't practical due to home configurations.

We also asked his ortho doctor to script for additional PT, so that helped as well.   Good weather is obviously the best to avoid dealing with snow and ice at a PT facility.  Dad got a lot more help there than with the nominal home help, but it still was very valuable.

Flooring:   is it carpeted?  If so, the older kind of thick, fluffy carpeting, shag I believe it was called?  Or is it flat and smooth?   Floors w/o carpeting can be slick, and falls can be more dangerous.    Throw rugs can also be hazardous.

Grab bars:   are they installed, and if not, please consider them, but only if they're installed by carpenters.  Although I've read here that others have used glue-on grab bars, I would never consider them.  You want bars anchored only in the studs to provide sturdy support, especially in the bathroom.  

Furniture:   are there clear paths throughout the home?   Obstacles can cause tripping.

Modifications:   walkers.   After Dad's second fall, we discussed options for protection, and decided to pad his walker, since he had once fallen on the legs of his walker.    Dad decided on pipe insulation, so we bought some, cut it to size and taped in on his walker legs.    When he fell in the future, it cushioned his legs not only from pavement or floor, but from the metal legs of the walker.

We also got a Life Alert pendant which Dad eventually took with him everywhere.    If you consider this, research, then contact the providers.   Some didn't even meet standards.   What I wanted was a provider with 24/7 service, levels of contact, and a good reputation.  

You'll see ads in AARP and on tv; check out these organizations like you would anything else.    I found in my research that not all of them met my standards, especially the ones that (a) only wanted to send literature or (b) took 2 - 3 days to return my inquiry call.

Emergency contact:    In addition to the pendant, Dad installed a lock box in the studs, outside, next to the front door.    If I wasn't available to get to Dad's home immediately, and the life alert service needed to call EMS, I gave them the combination to get in the house.

Medical:   is your father taking any medicine (such as Toprol XL) that can cause orthostatic hypotension, which affects someone's ability to safely rise from a seated position, and result in a fall?

Body strengthening:   Is your father still doing exercises?   If not, this is something my father found helpful, and I'd recommend it.    These arm and foot pedals can be used while seated at a table (arms) or while sitting (legs).    My father bought his from one of the mail order catalogues.  Less costly, but functional.   

Rehab facilities have the more sturdy and expensive versions, just as good but harder for an older person to lift and move.  My father had one like the model second from the left in the first row.     You might even be able to get one from a DME store if a physician scripts for it.

https://www.medicalexpo.com/medical-manufacturer/arm-leg-pedal-exerciser-50755.html

Lighting:   helps so much to illuminate interior areas and diminish tripping.  

Shoes:   good tread for gripping.

I forgot to answer your question as to staying at home!  My apologies.

My father was not interested and couldn't be persuaded to leave home, so we tried to accommodate, making a lot of changes, working with neighbors who checked up on him and called me if they were concerned.   I took him everywhere until some friends became involved, so I had a chance to assess his balance and coping skills, as did his friends and MOW people.   

It's hard to make the kind of assessment you face.   Perhaps you could establish criteria for remaining at home (living alone is always a challenge and you need to go back to work), but you can create at least a framework and nominal changes as posters have already suggested.   And monitor as well his progress, improvement and, hopefully, not deteriorations.

One concern I've had about elders living alone is stimulation; they often need contact, so consider that.   Dad looked forward to his MOW delivery people, and they provided insight and feedback to the coordinator who had a lot of experience (and a fireman husband) to assess an elder's skills.

When I came out, we went for walks to the local beaches, and at stores.   Dad shopped as long as he could when it was safe.

What kind of resources would your father have?   Neighbors?  Friends?  Church people?   All of these can provide feedback, monitoring as well as companionship.