POPA,
section 1983 can be exercised if you have your right to phone access denied(http://www.jailhouselaw.org/Chp2_Final.pdf), but I assume that is not what you are talking about. Which law is violated by a police man lying?
The only one I can come up with is depriving you of property(by making you pay a false claim), but thats in the declaration of independence, not the constitution.