The post also includes a direct quote from Healey during Thursday's debate in which the gubernatorial candidate states, "people should measure us by our record, by our actions."
Massachusetts Republican Party Chairman Jim Lyons on Friday called on Healey to respond.
"Voters deserve to know whether the attorney general and Democratic nominee for Massachusetts governor did in fact use her position as the top law enforcement officer in the state to pursue sexual relationships with state troopers serving under her," Lyons said. "This is a very serious allegation being made by Boston First Responders United, a group that includes individuals with special access to information about the goings-on inside agencies like the State Police.
"As the Democrats' candidate for governor of the commonwealth, Maura Healey needs to respond to these allegations as soon as possible."