This just isn't that black and white. It really depends on the circumstances.
As many have pointed out, it isn't legal to lie to the police about your name, date of birth or address, particularly when detained, and that is generally true in most states.
It generally is illegal to lie about a crime. If you falsely report a crime, you can and probably will be prosecuted, in most places.
If you are a witness to a crime and lie about what you saw, or fail to report a crime in some circumstances, you can be prosecuted, though this is tougher.
If you lie to law enforcement and your lies obstruct operations or cause an "emergency reaction," there are also applicable statutes that you can and will be prosecuted under, in many areas.
The feds also have a fairly general staute that used to be rarely used; it was explained to me that if you give false information to a federal investigator that is material to an investigation, that is a felony under federal law.
Results may vary according to local laws.
And yes, the police can lie to you, the courts have repeatedly held.