So just to clarify, you need a background check from the FBI and every state you have lived in? All I would do is send fingerprints and the letter?
...and whatever payment is required. If you want them to send the response other than first class mail you should also include a prepaid with sufficient postage - such as express mail - envelope for return.
How would you state what you need in the letter..? That you needed a background criminal check because you are applying for permanant residency in Canada? It's called a police certificate by Canada immigration but it's called something different in the U.S., isn't it??
Personally, I wrote a standard business format letter giving my name, stating I was going through the process of applying for permanent residency, requesting the criminal background check and my contact information.
I did the same for the FBI. However I saw this linked in another post on this forum
http://www.fbi.gov/filelink.html?file=/hq/cjisd/cover_letter.pdf which just takes filling in the blanks.
You are correct, Police certificate is what it's called by Canadian Immigration. Criminal History Background Check is what it's called in the US.