PA:
The match referee and officers investigated a complaint made by two Bolton fans against the United player after the match at the Reebok Stadium.
A spokesman for Greater Manchester Police said the investigation concluded no crime had been committed.
"During the Bolton Wanderers versus Manchester United game at the Reebok Stadium on Saturday April 1, a complaint was made by two Bolton Wanderers supporters of racist comments made by one player towards another," he said.
"An immediate investigation was commenced involving the referee which concluded that no crime had been committed.
"The matter is now closed."
It is understood police spoke to the players involved in the alleged incident after the game finished.
Ed. We do not know at the moment which players were alleged to have been 'involved'.