New York State has a law that says that landlords cannot prevent tenants from having a roommate.
Does this apply to the Mitchell Lama housing program?
I did find the following reference which stated this:
Do I have the right to have a roommate?
If you live in a privately owned building, and
If you are the only person who signed your lease (for rent control: if you are the only tenant of record),
Then you have the right to share your apartment with one other adult not related to you, and that person’s dependent children.
You do not have a right to a roommate if:
• you live in public housing or most subsidized housing, or
• if two or more people have signed the lease, and your lease does not expressly give you permission to live with an additional person.
There are additional considerations if you receive a rent subsidy (such as Section 8 or FEPS) or a rent exemption (such as SCRIE or DRIE), or if your rent is based on your income. Most programs require that you report what the roommate pays in rent as part of your income. Failure to accurately report this income can be a serious violation of the program's rules and could lead to termination of the program as well as legal actions. Also, bringing in a roommate may make your income too high to remain eligible for the program. Check your program’s guidelines before taking in household members.
However, it doesn't say anything about Mitchell Lama, and it goes on to say things like:
If you are a rent-stabilized tenant, you are prohibited from charging a roommate more than a proportionate share of the rent.
Which suggests that rent-stabilized apartments do allow roommates (I'm guessing then that rent-stabilized apartments are not 'subsidized housing')