If you are being officially questioned, there are only two things you need to say -
1. Am I under arrest?
2. I wish to speak with my lawyer.
Very simply because they think you were either involved with or the prime suspect in a crime, and -
1. The police officer is trying to solve a case/send something to the DA, and that is their first priority, the lawyers/court are there to determine what happened.
2. Even if they don't get a confession for a serious crime, they may charge you with whatever they can, to provide time to find more evidence.
3. They have no obligation to tell you the truth or provide any information they have.
The only way to get any view of what is going on is to involve a lawyer.