A spokesperson for the RCMP in Manitoba told ESPN.com that, as of Tuesday, no charges have been brought against Richards but declined to comment further.
The source said Canadian Border Services is also involved in the investigation, but a spokesperson declined comment, citing Canadian privacy laws.
The incident occurred on the border of Emerson, Manitoba, and Pembina, North Dakota.
Richards, a two-time Stanley Cup champion, had the remaining five years of his 12-year contract terminated Monday by the Kings. The team did not say why Richards was in violation of the deal other than to say in a statement that it was for "a material breach of the requirements of his Standard Player's Contract."
Several sources told ESPN.com that the Kings were made aware of the situation involving the Canadian authorities Friday, approximately an hour after the first round of the 2015 NHL draft had begun.
According to a source, the Kings did inform the league about their intent to terminate Richards' contract, even before putting him on unconditional waivers Sunday. The NHL Players' Association has a right to file a grievance for Richards and is in the process of gathering information before deciding whether to go that route.
"We are in the process of reviewing the facts and circumstances of this matter, and will discuss the situation with the player in order to determine the appropriate course of action," NHLPA spokesman Jonathan Weatherdon said Monday in a statement.
Should the NHLPA decide to file a grievance within a required 60-day deadline, the dispute would be heard by an impartial arbitrator, as governed by Article 17 of the collective bargaining agreement.
It is not immediately known the legal grounds upon which the Kings' decision hinges, although Article 2 (e) of the Standard Player's Contract states that a player agrees "to conduct on and off the rink according to the highest standards of honesty, morality, fair play, and sportsmanship, and to refrain from conduct detrimental to the best interest of the Club, the League or professional hockey generally."
Article 14 of the SPC states that a club can terminate the contract if a player shall "fail, refuse or neglect to obey the Club's rule governing training and conduct of Players, if such failure, refusal or neglect should constitute a material breach of this SPC."
Los Angeles had been in the process of trying to trade Richards -- discussions were in place with both the Edmonton Oilers and the Calgary Flames -- but Kings general manager Dean Lombardi immediately informed both teams upon learning about the situation that he had no prior knowledge of the incident and halted those talks.
"He came right over to me," Oilers general manager Peter Chiarelli confirmed to ESPN.com. "He pulled me aside and said, 'Hey, Pete, this is going to come out. I had no idea. This is important you know so that talks [don't go any] further.'"
Lombardi did the same with Flames GM Brad Treliving on the draft floor, Treliving confirmed.
It is not immediately clear when the incident took place.
Richards was earning $5.75 million per season as part of a $69 million deal that was scheduled to run out in 2020. The 30-year-old veteran had cleared unconditional waivers Sunday. The deadline for the first buyout window is June 30.
ESPN.com's Craig Custance contributed to this report.