LANSING, Michigan (Reuters) - The Michigan House of Representatives on Tuesday gave final approval to a second "right-to-work" law covering private sector union workers such as the automotive industry, after earlier passing a separate law on public sector workers.

The Republican-majority House passed the private sector law by a vote of 58 to 52.

"Right-to-work" laws make membership of a union and payment of dues voluntary. Their approval in Michigan, the home of the U.S. auto industry and a stronghold of unions, is a major blow to organized labor in the United States.

The measures now go to Republican Governor Rick Snyder, who is expected to sign them into law in the next few days, making Michigan the 24th right-to-work state.

(Reporting by Bernie Woodall and David Bailey; Editing by Greg McCune)