In Maine it is called "false swearing" and punishable with imprisonment up to 4 years.
The only time I heard of a conviction on "false swearing", in this liberal state, though, was when a tax activist was found to have included a few unverifiable signatures on an anti-tax petition.
Oh, it's against the law, all right, but the DAs choose which laws to enforce and who to apply the law to. That's a huge problem.
I just looked it up: http://janus.state.me.us/legis/statutes/17-a/title17-asec509.html
Filing a false police report in the state of Maine is a class D crime which carries a sentence of less than one year, which equates to a misdemeanor in states using that terminology (ME doesn't use the terms "misdemeanor" and "felony"). Perjury in court or signing governmental documents under penalty of perjury is a felony.
I just read of a Portsmouth woman who was arrested and charged with filing a false report of rape a few months ago. It is a a misdemeanor charge: http://www.seacoastonline.com/news/07122006/nhnews-ph-p-fake.rape.html