No charges have been brought against Richards, who hails from Kenora, Ont., ESPN reported an RCMP spokesman as saying.
Canadian Border Services is also involved in the investigation, according to the report.
A two-time Stanley Cup winner with the Kings, Richards, 30, had the final five years of his 12-year, $69-million US contract terminated Monday by the team, which declined to comment on why the unusual move was made.
Once considered a star during his time with the Philadelphia Flyers, Richards's production has tailed off in recent years. He managed only 16 points in 53 games with the Kings last season and was sent to the minor leagues for a time.