Broward politicians are continuing their infighting over a proposal to create a special taxing district to fund school safety — demonstrating how difficult it is to find consensus solutions after Connecticut’s Sandy Hook tragedy.

On Tuesday, Broward School Board members approved sending a letter to state Sen. Eleanor Sobel, D-Hollywood, objecting to her proposed solution for staffing police officers at every public school. Sobel has filed a pair of bills in the Legislature this year that could pave the way for additional property taxes in South Florida and across the state. The additional property tax (up to 50 cents on every $1,000 of taxable value) would pay for more school police officers and mental health services.

A local voter referendum would be required before any county could levy the tax.

“This is almost the equivalent of killing a fly with a sledgehammer,” Broward Schools Superintendent Robert Runcie said.

Runcie and School Board members argue that increased police officer staffing can be achieved without asking taxpayers to dig into their pockets, and the school district is also worried about losing control over school safety decisions. Sobel’s new taxing district would create a special governing board to oversee the money — School Board members would be on that board, but so would city, county and state politicians.

“Everything has been taken out of our hands,” School Board member Robin Bartleman said.

Broward’s school leaders also say Sobel’s proposal could lead to property tax fatigue among voters, and make it harder for the district to win voter approval for a school construction/repairs bond issue. Though no date for a bond issue vote has been set, it’s clearly something that the school district would like to eventually ask of voters.

Sobel on Tuesday stood by her school safety proposal. Sobel said Broward will struggle to fully staff school police officers without the new taxing district, and she said it can happen at the same time as a construction bond issue.

“Maybe both are important,” Sobel said. “Why don’t you put it out there and let the voters decide?”