AUSTIN, Texas — Texas election officials have acknowledged that hundreds of people were allowed to bypass the state’s toughest-in-the-nation voter ID law and improperly cast ballots in the November presidential election by signing a sworn statement instead of showing a photo ID.

The chief election officers in two of the state’s largest counties are now considering whether to refer cases to local prosecutors for potential perjury charges or violations of election law. Officials in many other areas say they will simply let the mistakes go, citing widespread confusion among poll workers and voters.

The Texas law requires voters to show one of seven approved forms of identification to cast ballots. It was softened in August to allow people without a driver’s license or other photo ID to sign an affidavit declaring that they have an impediment to obtaining required identification.

Even after the affidavits were introduced, voters who possess an acceptable photo ID were still required to show it at the polls.

The revelations come as President Donald Trump makes frequent claims that the nation’s voting systems are vulnerable to fraud. The president has repeatedly said, without citing any evidence, that he would have won the popular vote if not for 3 million to 5 million immigrants in the country illegally who voted for his Democratic opponent, Hillary Clinton.

An Associated Press analysis of roughly 13,500 affidavits submitted in Texas’ largest counties found at least 500 instances in which voters were allowed to get around the law by signing an affidavit and never showing a photo ID, despite indicating that they possessed one.

Others used the sworn declarations to lodge protest statements against the law.

One affidavit from Hidalgo County, along the Texas-Mexico border, read: “Did not want to ‘pander’ to government requirement.” In Tarrant County, an election judge noted on an affidavit: “Had photo ID but refused to show it.”

“If we see that somebody blatantly says ‘I have ID’ and refused to show it, we’re going to turn that over to the D.A.,” said Stephen Vickers, chief deputy elections administrator for Tarrant County, which includes Fort Worth. “If they tried to use the affidavit to get around the system, yeah, I see that as a violation.”

The disclosures came as top Texas Republicans cheered the case of a Mexican national who was sentenced to eight years in prison for illegal voting. Rosa Maria Ortega was convicted earlier this month on two felony counts of illegal voting over allegations she improperly cast a ballot five times between 2005 and 2014 in Tarrant County. Her attorney has said Ortega was a permanent U.S. resident who mistakenly thought she was eligible to vote.

Gov. Greg Abbott and Attorney General Ken Paxton, both Republicans, cited the case as proof that voter fraud is real and requires preventive measures.

The govenor’s office did not return a request for comment from the AP.