Since we don’t have all of the facts, I’ll just say that generally it’s possible, the police may very well have the right to enter your home.
If this is in the U.S., there is a general exception to Fourth Amendment search protections where the police reasonably believe that there is an imminent threat to a person’s safety or evidence of a crime is being destroyed. Concern about someone committing suicide, particularly when a person who knows the person has reported the possibility, may very well create a reasonable concern.
The thing is, there are a few things that happened here, and each requires a certain level of underlying suspicion or concern for the police:
(1) The police entered your home.
(2) The police detained you in your home.
(3) The police searched your home thoroughly.
(4) The police interrogated you.
(5) The police took you into custody.
A legal problem may very well have arisen when they did a search of your home and interrogated you while you were being detained, leading to your being taken into custody.
Attempting to commit suicide is a crime generally. So detaining you in your home while you are intoxicated and asking questions may be an interrogation and therefore you may have needed to be informed that you had the right to an attorney. If you weren’t mirandized, then it’s possible that your rights were very well violated.
The question is, however, do you want to get involved in all that? Maybe – you might want to talk to a lawyer about this.
@YoBob – Not really. A warrant can be issued upon probable cause, However, entry without a warrant really requires exigent circumstances (like those I mentioned). The information may have provided them with sufficient knowledge that exigent circumstances existed that gave them the right to enter the home without a warrant.