I recently had 2 tenants bring in boyfriend/girlfriend roommates. I had each of them do the whole process: application, background/credit check. I then just did an amendment to their leases that states that new roommate can live there, but original tenant is responsible for apartment and full rent, and that upon landlord or tenant asking them to leave they have 24 hours to vacate property. I didn't want to deal with breakups and having them decide who stays and who leaves and who is responsible, bla, bla, bla, lol! I've had to deal with this before and it's not fun. Sounds like yours is just a regular roommate. I guess maybe I would make sure that they BOTH can afford the apartment on their own, and state that upon one tenant leaving, with appropriate notice, that the other will be 100% responsible or something like that, and can find another approved roommate if they want. I do month to month leases though. I just don't want miserable people to have live together if they don't get along. I realize that's not my problem, but it would become the building's problem if they are yelling and fighting.
One other clause might be that the deposit runs with the lease and if one moves out early that they are responsible for getting their half of the deposit from the other, or their new roommate.
You just have to do what you think would work for you and your business. It can be tricky! Good luck!