The remit asks the Government to increase police resourcing to ensure adequate staffing and coverage for New Zealand communities, and that police chiefs are not forced to compromise community policing because of budget constraints.
In this year's Budget, police received a nearly $300 million boost to fund pay rises, but no funding for new recruits.
As Hastings District Mayor, Mr Yule, said his council had spoken with police and while they were restructuring and using new technology, they did not have the capacity for less serious crime or what Mr Yule called safety issues.
"There are similar concerns from other communities like Lower Hutt, Napier and Tararua," he said.
In response, Hastings District Council installed CCTV in the district, established the City Assist ambassadors and organised community and security patrols, at a cost of nearly $1 million per year.
"Many councils have volunteers going out in cars or have funded cameras and other security initiatives," Mr Yule said.
"Is it actually the role of local government or is this the systemic underfunding of the police that has ended us up in this situation?"
The value of community policing was often underestimated, he said, and LGNZ was keen to discuss how the Government would approach this issue. "We need that local knowledge and connection that comes from community policing. Communities need to feel safe to thrive."
In their quarterly media briefing, LGNZ also announced a new independent standards system to measure the performance of local authorities had been well received by the local government sector, and $12 million would be spent over four years to fund local infrastructure to support tourism, co-funded by local authorities facing infrastructure stress from increased tourism.