When is it a crime, not to report a crime?

If a public official knows about a crime against his government, is he obligated to report that crime and to cause a thorough investigation into it and to pursue charges, if warranted?

If the crime is a felony, for what reason would the official not make it known to the public? Law enforcement agencies throughout McHenry County are routinely contacted about crimes against persons and against property, about thefts of thousands of dollars. They investigate and confer with the State's Attorney to determine whether felony charges are warranted. 

I got to thinking more late this evening about this question.

What is it called when no action is taken upon discovery of a crime involving the theft of government property? Can a County department sweep a felony under the rug and handle it administratively and at a low enough level that eliminates public reporting?

Isn't it a more serious crime not to report it than the crime itself? For what purpose would a senior government official not take normal and full law enforcement action against any perpetrators?

What would such lack of action be called? Malfeasance of office? Dereliction of duty? Would it rise to the level of abuse that the senior official(s) in that office or department should be sanctioned? Removed from office? Investigated and charged themselves?

What if a pattern of such failures was uncovered? How big would the shake-up be?

And if officials began cutting and running, to avoid prosecution, shouldn't they be charged and prosecuted, anyway, even if they have slipped away into retirement?

A bank robber doesn't avoid prosecution by saying, "Oops. Sorry. I'll just return the money, when I can."

There are men and women in McHenry County and right here in Woodstock who know what I'm talking about. Let's hope they will comment and add information.