When you have an adult child on the high-functioning end of the autism spectrum, you want to encourage them to have as much independence as possible. It is important to you to regain your free time and not have to worry about this adult child all the time, and it is important to your adult child that they find their way in the world on their own. Apartment rentals of all kinds exist, but given the special circumstances here, you might want to follow some specific suggestions.
Testing the Waters with a Short-Term Rental
To see if your adult child with ASD can navigate daily living without you having to do everything for them, try a short-term apartment rental near your family's home. A one- or two-week rental should be enough to see if your son or daughter can manage tasks by themselves. If they work a job, then they can use money earned from work to rent the apartment and pay the proprietor what is required. Whether or not you choose to disclose to the proprietor your son's or daughter's diagnosis is up to you. Some parents feel it is safer not to mention it, while others feel it might be helpful if the proprietor knows and can occasionally check up on their child.
Moving on to Something More Long-Term
If your son or daughter manages the tasks of daily living in the short-term apartment, find an apartment where they can live on a month-to-month rent basis. A one-bedroom is sufficient, as it will provide your child with enough space while making sure they do not have to share said space with a roommate that might exacerbate some of their ASD symptoms. If there is an apartment manager, it does help in this case to disclose the ASD diagnosis because then the apartment manager can help remind your child of rent payments and keep a lookout for their safety where the other tenants are concerned.
Your son or daughter will have to show that they can consistently maintain the apartment and look after themselves with little assistance. They will also have to consistently pay rent every month, and a little training on managing money, banking, and writing a check for rent will go a long way. After a couple of months, they should be doing just fine and managing things on their own. If not, it might help to look at other apartment arrangements.