As a crime scene investigator or forensic scientist you will often be in a position to handle drugs and cash (sometimes very large quantities). You will also have to testify in court on these matters. It makes no sense for an agency to hire someone with drug or credit problems, or has any other kind of arrest record (DUI, domestic violence, etc.). That is the major reason agencies do background investigations on candidates.
Every agency that I know will disqualify a candidate that has been convicted of a felony.
One thing you might want to do is identify the agency you might want to work for, and contact the person at the agency who does backgrounds. Tell that person your situation and see what they say and/or recommend.