Gov Charlie Baker on Friday vetoed a bill that would expand the power of public sector unions, citing employee privacy.

It is the second time Baker has returned the bill, H.3854, to the Legislature unsigned.

It would take a two-thirds vote of the Legislature to override the governor’s veto. Since lawmakers are on their summer recess, that cannot happen until at least September.

The Legislature passed the bill in response to the U.S. Supreme Court’s decision in Janus vs. AFSCME, which ruled that government workers cannot be forced to pay union dues.

The bill would let unions charge nonmembers fees for representation in grievances.

But the bill would also give unions a range of new rights, including access to public employees’ personal contact information. Those additional rights have been controversial, with some business-backed organizations worrying that they would open workers up to potential union harassment.

Baker wrote in his veto letter to the Legislature, “While I have supported changing Massachusetts law to address recent changes in how public sector unions work with non-union members, including allowing public sector unions to charge non-members for costs associated with representation in grievances and updating some of the rules of engagement between state employees and public employee unions, I refuse to sign legislation that compels state and municipal government to turn over the cellphone numbers of private citizens, who happen to be government employees, without their permission, to private organizations.”

After the Legislature first passed the bill, Baker, a Republican, sent it back with a number of proposed changes. But the Democratic-led Legislature rejected those changes and returned it to his desk, leading to Friday’s veto.

Cristopher Carlozzi, state director of NFIB Massachusetts, a small business group, applauded Baker’s veto. “The Governor offered a very commonsense amendment that provided labor unions an opportunity to collect their reasonable fees, while still protecting the rights of workers,” Carlozzi said in a statement. “The legislature chose to pacify a handful of labor leaders, rather than address serious privacy concerns for public employees.”