PHOENIX — Backers of a referendum challenging election- law changes filed suit Friday against Pima County Recorder F. Ann Rodriguez and her counterparts in two other counties.

Attorney James Barton contends the election officials in Pima, Pinal and Cochise counties improperly disqualified some of the signatures on petitions. The reasons given ranged from saying the person was not registered at the address listed to the signatures or other information being illegible.

Barton said a review by referendum organizers shows that at least 80 of those voided signatures are valid.

While the fight is over a small number, it could make or break the effort to let voters decide whether to overturn election-law changes pushed through earlier this year by the Republican-controlled Legislature.

The signatures are part of a 5 percent random sample given to each county. So voiding 80 signatures knocks 1,600 names from the total.

And with other counties still to weigh in, including the state’s largest county, referendum backers want to preserve as many signatures as they can.

The law being challenged would limit who can take someone’s early ballot to a polling place, impose stricter requirements on citizen groups proposing their own laws through initiatives and require minor party candidates to get more signatures to get on the ballot.

Backers turned in more than 146,000 signatures. An initial screening by Secretary of State Ken Bennett cut that to 139,161.

Referendum organizers need to have at least 86,405 valid signatures after final verification to keep the law from taking effect until voters get a chance to review it at the 2014 general election.

Spokesman Robbie Sherwood said the group had to sue the three counties now, even though others have yet to complete signature verification, because state law provides only five days to challenge any county’s findings.