WITH POLLS showing Massachusetts voters highly concerned about abortion rights, candidates for office – even for down-ballot jobs that seemingly have little to do with the issue – are coming up with ways to demonstrate it’s a high priority. 

Tanisha Sullivan, a Democratic candidate for secretary of state, made abortion rights a centerpiece of her campaign on Monday, pledging to use the office’s oversight of public records, corporations, and lobbyists to protect abortion rights in Massachusetts.

If elected, she vowed to give companies seeking to do business, issue a security, or raise funds in Massachusetts a “reproductive health grade” based on information she would require the firms to provide on the health plans they offer, the child care they provide, or their cooperation with law enforcement officials to “punish anyone seeming or aiding reproductive health services.” 

In a debate with incumbent Secretary of State William Galvin on Monday, Sullivan labeled her opponent “anti-abortion” and said the office should be on the front lines of the abortion rights fight. Galvin disputed Sullivan’s characterization of him, saying he believes abortion “is a personal decision of the woman.” 

In the Democratic primary race for auditor, both candidates are strong supporters of abortion rights, yet Sen. Diana DiZoglio of Methuen has tried to suggest her rival Christopher Dempsey is insensitive on the issue.

Dempsey wanted to bring greater transparency to the campaign by releasing all of his answers to questionnaires issued by special interest groups trying to decide which candidates to endorse. He urged DiZoglio to release her questionnaires as well. 

DiZoglio said she would, with one exception. She said she wouldn’t release the questionnaire of Reproductive Equity Now because the group wanted it kept confidential and releasing it would endanger  lives.

“It’s unfortunate that Chris Dempsey irresponsibly issued a press release for pure political gain without considering the damage that could be done by such dissemination — especially after the overturning of Roe v. Wade and the ongoing battle to protect reproductive rights here in Massachusetts and across the country,” DiZoglio said in a statement.

The issue appeared to fizzle when Dempsey said he didn’t release the Reproductive Equity Now questionnaire because of the organization’s concerns, but was working with the group to find some sort of solution. On his campaign website, it says “coming soon” next to the questionnaire of Reproductive Equity Now. 

Reproductive Equity Now said its chief concern was the precedent it would set. Officials at the organization say they worry mostly about protecting the confidentiality of candidates who share personal stories about abortion in their answers. 

At a debate Monday night, DiZoglio accused Dempsey of lying when he promised to release all of the questionnaires and then not releasing the Reproductive Equity Now document. DiZoglio, meanwhile, released a few more of her questionnaires. She said she is asking each group for permission to post them.

In the Democratic primary for attorney general, all three candidates have promised to be vigilant in supporting abortion rights. Some of their ideas are unusual. 

Shannon Liss-Riordan, for example, said her office wouldn’t do business with any company located in states where abortions are banned if the firm fails to cover travel costs for employees seeking reproductive health care in another state.

Andrea Campbell said she would create a special reproductive justice unit inside the attorney general’s office and also set up an abortion hotline for people seeking information on their rights as well as reproductive health services. 

“Having a one-stop shop for folks to also be able to engage I think is really important, and again, I think an opportunity for the AG’s office,” she told MassLive.