As a police officer in a small Oregon town in 2004, Sean Sullivan was caught kissing a 10-year-old girl on the mouth.

Mr. Sullivan’s sentence barred him from taking another job as a police officer.

But three months later, in August 2005, Mr. Sullivan was hired, after a cursory check, not just as a police officer on another force but as the police chief. As the head of the department in Cedar Vale, Kan., according to court records and law enforcement officials, he was again investigated for a suspected sexual relationship with a girl and eventually convicted on charges that included burglary and criminal conspiracy.

“It was very irritating because he should never have been a police officer,” said Larry Markle, the prosecutor for Montgomery and Chautauqua counties in Kansas.

Mr. Sullivan, 44, is now in prison in Washington State on other charges, including identity theft and possession of methamphetamine. It is unclear how far-reaching such problems may be, but some experts say thousands of law enforcement officers may have drifted from police department to police department even after having been fired, forced to resign or convicted of a crime.