After you finally get back into your apartment, the phone will ring; answer it to talk to Dr. Quentin, your late aunt's physician. Once you've done that (or looked at the letter from him in your inventory), you'll find Bellevue Psychiatric Hospital on the map when you leave your apartment.
At Bellevue, go right through the arch to speak to the guard. Tell him you want to see Dr. Quentin (he didn't know your aunt, by the way), and he'll let you in.
Every time you come here, you need to check in with the guard, but you won't have to prove your identity again.