The U.S. Constitution provides some very clear guarantees regarding the rights of the accused and of their due process of law. The standard for convicting someone of a crime is assumption of innocence until the burden of proof of guilt beyond reasonable doubt is met by the prosecution.
It most certainly is a crime to falsely accuse another person of felony wrongdoing by knowingly making bogus claims to the police. Let's assume that an innocent person is convicted of a crime based on such a bogus claim as well as knowingly false testimony in court (perjury). Should the false accusation be discovered then there is a process by which:
1) the innocent person can appeal to have his conviction overturned* and other possible remedies instituted.
2) the person making the knowingly false accusations can be prosecuted and, if found guilty in accordance with due process of law, suffer the appropriate sentence as proscribed by criminal statute.
3) the person who is harmed by being falsely accused may sue the accuser in civil court for loss. Here, the burden of proof is less than for a criminal case.
This process is not automatic. The legal (as well as financial) burden for overturning a wrongful conviction lies with the convicted. Prosecution of the crime of false accusations or perjury is at the discretion of prosecutors, who will usually decide whether to prosecute based on the their estimation of likelihood of gaining a conviction. In reality, other factors come into play, such as the expected public reaction to prosecuting the false accuser who may be a sympathetic character in some way.
In the Duke University gang rape case, for example, the woman making the false charges was not prosecuted because it seems as if she had some serious psychological issues as well as substance abuse issues. In addition, it also appears that the prosecutor himself knowingly participated in the fabrication of false information for the purpose of making himself a more appealing candidate during his re-election campaign.
Generally speaking, prosecutors are virtually immune from being prosecuted themselves for misconduct that results in a false conviction, but there are exceptions, if the misconduct is grievous enough (and if the wrongfully convicted has a lot of money or clout).
*
The Innocence Project is a non-profit group that has successfully assisted hundreds of wrongfully convicted persons in proving their innocence and getting their convictions overturned. They also advocate for systematic reforms to the criminal prosecution process.
http://www.innocenceproject.org/
http://en.wikipedia.org/wiki/Innocence_Project
These people are truly awesome and it's one of the very few causes that I regularly donate to. I try to spread their word as often and as far as I can.