Reporting crime is certainly a public service, but is there any legal obligation for you to report a crime if you see one?
You may recall the series finale of "Seinfeld," in which the four New Yorkers were arrested in Massachusetts under a fictional law that made it an arrestable offense not to rescue someone whom they see being carjacked. And while that episode devolved into a comical courtroom scene, many viewers may have been left wondering if they could be arrested for doing the same.
So do you have to report a crime if you see one?
Duty to Rescue: Generally Civil not Criminal
The legal duty to rescue does not exist for civilians, and unless you are an emergency responder (police, firefighter, EMT, etc.), you likely will not be held accountable for failing to rescue a victim of a crime. However, if you are in one of these specified roles or you happen to be the parent of a child in danger, you may be held accountable for refusing to offer help -- even if it's simply by calling 911.
Even if you are held civilly responsible for failing to rescue someone, it's more than likely that this legal responsibility will not end in a criminal charge. These failure to rescue cases are handled almost entirely in civil court, and do not involve any allegations of criminal liability. However, if you are a parent, you may be arrested for abuse or neglect if you fail to report that your child is the victim of a crime.
Civilians Who Fail to Report
If you look out your window and see someone getting mugged, you're not likely to be hauled in for conspiracy. However, there are situations wherein your silence or inaction may be taken as complicity or cooperation in a criminal scheme. Think mob wives and RICO cases.
Cops' Duty to Report
Police officers in general have a wide scope of discretion as to what crimes they choose to report -- especially in urban areas. Police may be ethically bound to report all crimes, but there isn't typically a criminal or civil law that punishes not reporting. Arizona's SB 1070 and its ilk have sought to create a right for civilians to sue cops who do not report illegal immigrants, but these laws are largely unenforceable.
So while it's a good idea to report crimes, you aren't likely to be arrested if you fail to do so.