By Jon Herskovitz

AUSTIN, Texas (Reuters) - An Austin City Council member who is a supporter of ride-hailing companies Uber [UBER.UL] and Lyft has filed a lawsuit to overturn a requirement for their drivers to undergo fingerprint criminal background checks approved in a May municipal vote.

Donald Zimmerman filed the suit against the mayor on Thursday in a Texas district court seeking to overturn the May 7 ballot initiative, arguing its language was confusing, unlawful and did not provide enough information about fingerprint criminal background checks for drivers.

The two companies campaigned against the requirement, which they said was an unnecessary and costly barrier to entry for new drivers. They said their own background checks are comprehensive and ensure safety.

Uber and Lyft spent more than $9 million in their failed attempt to defeat fingerprint requirements in Austin's May 7 vote, making it the most expensive political campaign in the city's history.

The two companies halted service in Austin shortly after the vote, putting about 10,000 of their drivers out of work.

The Texas Supreme Court in March denied a motion to halt the Austin election brought by a plaintiff who argued the ballot language was confusing and unlawful. The mayor's office has said it stands by the ballot language.

Former Uber Technologies Inc and Lyft Inc drivers in Austin filed lawsuits this month in federal court in San Francisco, accusing the ride-hailing companies of breaking a federal law by abruptly halting operations in the city.

Many former Uber and Lyft drivers have since joined start-up, ride-hailing firms currently operating in the city.

(Reporting by Jon Herskovitz; Editing by Cynthia Osterman and Andrew Hay)