General Motors Co. will recall about 7,600 Chevrolet Caprice police vehicles for a transmission issue, making this the 75th safety recall action the auto maker has taken this year and putting the number of total vehicles recalled by the company in North America at well over 30 million.

The recall, posted by the National Highway Traffic Safety Administration on Tuesday, covers certain 2011 through 2013 model year Caprices. The…