IANAL, but my understanding is that in some jurisdictions, lying to the police is Obstruction of Justice.
In addition, lying to the police can be de-facto illegal by being the primary evidence they have that you are guilty of some other crime "Why would s/he lie if s/he weren't guilty?".
In addition, lying to the police can be de-facto illegal by being the primary evidence they have that you are guilty of some other crime "Why would s/he lie if s/he weren't guilty?".