You are under absolutely NO obligation and in fact, it's often a horrible idea to talk to them. I know - you're wrongfully accused and want to clear your name, but anything you say can be used against you. Worse case scenario? You protest your innocence and they write down your statement incorrectly. Months or years later when your case goes to court, they will have no memory of it and just look at their report, shrug and say, "Well, this is what you told me - see? It's in my report."
If you're under investigation, keep quiet and get an attorney ASAP. Do NOT discuss anything about these allegations with ANYONE except an attorney in a confidential communication.
Under the 5th Amendment you do not have to give a written or oral statement or be interviewed by law enforcement. Hire a criminal defense lawyer before you do anything else.
If the dectectives give you a miranda warning keep your mouth shut, it is their job to prove you did it, do not help them. Only have your lawyer speak for you. If you lie to them that will become a seperate offense.
If you are arrested tell the arresting officers your want to talk with your lawyer and do not say anything else, be polite and respectful the police have a tough job, do not aggreivate matters.
