City Councillors are expected to turn up the heat on proposals for medical marijuana dispensaries in Boston next month. A hearing is scheduled for March 4 at City Hall.

State public health officials have given the initial sign-off to dispensaries at 70 Southampton St., operated by Green Heart Holistic Health & Pharmaceuticals, Inc., and at 364 Boylston St., operated by Good Chemistry of Massachusetts.

But several councillors, including At-Large member Stephen Murphy and District 7’s Tito Jackson, cried foul last week, according to UniversalHub.com, saying the backers of the dispensaries did not accurately portray their stances on the proposals when dealing with the state Department of Public Health. The councillors, including District 3’s Frank Baker, remain concerned about how the dispensaries received their licenses to operate and how the locations were picked.

The outlet proposed for Southampton Street was also a top item on the McCormack Civic Association’s agenda on Tuesday night. Desmond Rohan, an executive board member, said the location has the potential for abuse and for pulling away police resources, since there is a methadone clinic and a homeless shelter in the same area. “It’s like putting candy in front of a kid,” Rohan said. “I just think the location isn’t ideal.” He also noted that Green Heart has not reached out to the civic association about its location.

Councillor At-Large Michelle Wu, who attended the association meeting, said the dispensaries, wherever they land, will bring a “big change” to the area. “It’s important for us to recognize that the medical use does help people,” she said. “But it’s a delicate balance in our neighborhoods.” Wu said she hopes to learn more about the proposals at the March 4 hearing.

The area between Newmarket and Andrew Square, which is close to the proposed location, already has public safety issues, according to South Boston state Rep. Nick Collins, who said he has concerns about how prescriptions for medical marijuana will be monitored. He said he hopes to file legislation to clarify the law that is on the books. “This is not easy, trying to put together regulations and trying to manage the introduction of a new prescription drug to the market,” he said.

A statewide ballot question approving the use of medical marijuana won overwhelmingly in 2012. In Boston, the margin was 69 percent for the measure and 30.7 percent against it.