There are exceptions to this, however 99% of the time your only answer to a LEO needs to be, "I don't answer police questions. I want a lawyer."
If you've ever seen the video at the end of this article (I suggest you watch it), Mr. James Duane gave this speech, "Don't Talk to the Police." Mr. Duane has released a book to update and clarify his remarks from this video. You Have the Right to Remain Silent is scary reading, much like a Stephen King novel.
In the many talks Mr. Duane makes on this subject, he asks if any of those in the audience have a parent who is a Law Enforcement Officer (LEO) or Prosecutor. Mr. Duane then writes this:
In almost every group, there is at least one student who tells me that his father is a state trooper, or that her mother is a prosecutor. Every time this happens, without exception, the student in question has told me basically the same thing: “Years ago, my parents explained to me that if I were ever approached by a law enforcement officer, I was to call them immediately, and they made sure that I would never agree to talk to the police.” (Most of these young people also volunteered that their parents in law enforcement advised them to never allow an officer to search their apartment or car, but that is the subject for another book.) Not once have I met the child of a member of law enforcement who had been told anything different.
Yet, the police want us to talk to them.
Mr. Duane then relates numerous stories where an unclear statement leads to being prosecuted and years in prison. The most egregious example was this: a picture of a Confederate flag was placed on a Black workers desk. Poor taste, yes. Offensive, certainly. Was it a crime? Maybe. A federal LEO investigating the incident asked a co-worker of the victim, who denied committing this act. She was charged, not with a hate crime or something else born on this offensive incident, rather "lying to investigators." Martha Stewart didn't go to prison for insider trading, she went for "lying" to prosecutors.
BTW, "lying to investigators" can be as simple as using different adjectives to describe something or someone. In your first statement you say, "The perpetrator was bald." Then in a later interview with another investigator, you say, "The perpetrator had close-cropped hair." That right there is enough to get you a lying to investigators charge, maybe even obstruction of Justice. A literal 1/16" of hair and how you describe it can land you in federal prison for years.
I also learned something new from reading this. Mr. Duane also relates that anything incriminating you say to the police is admissible in court as to your guilt. Anything that exonerates you (proves your innocence) is called hearsay and is not admissible in court (this I already knew). In this book, he explains the why: It is solely the responsibility of the prosecutor to present the facts of the case. The defense can ask clarifying questions, grill the witness and their words, cast doubt on the veracity of the evidence, but the defense cannot introduce their own facts, in this case the exonerating statement.
The payoff of the entire book is this:
The bottom line is clear. Even if you are innocent, the police will do whatever it takes to get you to talk if they think that you might be guilty. That includes saying just about anything, no matter how dishonest, to help persuade you that it might be in your best interest to give them a statement. And the courts will generally say whatever they need to say to excuse the dishonesty on the part of the police, even if the courts have to say something that is just as dishonest. This ought to be a national scandal and not swept under the rug the way that it is. This is not a legal system that is deserving of our respect, much less our cooperation. If a used car salesman engaged in this sort of deception, he would be thrown behind bars. It boggles the mind that we regularly allow police officers to do the same sort of thing to our children—but of course we’re only allowing it because we don’t know that it is going on.
That should get you very angry.
The sage advice is given on the in the last section. I won't spoil it so you have to get the book. It's free in Kindle format on Amazon Prime.
Now, there are a couple of exceptions I must in good conscience put forward. If you are involved in a traumatizing incident, (very bad car crash, self-defense shooting, etc.) For this, I defer to another person whose words I trust. You tell the police, "I am the victim here. I will give a statement and fully cooperate once I have consulted with my attorney."