This has happened to me three or four times because I was stupid enough to trust my "friends". Cops are the scum of modern civilization IMO. They persisted and threatened me if I didn't let them into my room. After I let them in they just inspected what I had in the room and asked me questions. I convinced the cops I was fine a few times and sometimes I could not, when I could not, they threatened to take me to a hospital forcibly if I didn't do it voluntarily.
That was my experience with cops. so I think the best thing to do would be to firstly avoid having cops called on you (Do not use suicide hotlines, tell your friends how you feel if you don't trust them). But if somehow cops are in front of your door, maintain composure and try to convince the cops that you are not going to harm yourself in any way and convince them that you do not have anything in your room that can be used for the purpose.
I would probably just politely decline and tell them to leave. They can't make me let them welfare check me, right?
in my experience they made me. they said they will have to use force if I don't comply. I was even handcuffed once when I declined to go to the hospital with them. I am from Canada though, my guess is American and Canadian cops are pretty similar.