This holiday season, the story for New Haven may be “How the budget cuts stole Christmas.”

The elimination of the city’s Christmas tree on the Green is a stirring signal of fiscal austerity as the mayor presented $6 million worth of new cuts to next year’s budget. And it’s not all tinsel and tassels: The proposed reductions will hit the city’s public schools and police department.

The cuts, which Mayor John DeStefano Jr. announced at a press conference Monday, come after complaints from city residents, including members of activist group New Haven Citizens Action Network, about the tax increase in DeStefano’s earlier proposal, which would have increased the average homeowner’s taxes by 8.8 percent and 15 percent for the average condo. With Monday’s amendment, the proposed budget only increases taxes by 4 percent, or $18 per month, for the average homeowner.

Even so, the amendment cuts the mounted police unit, the presence of district managers at management team meetings and public safety hires. DeStefano said Monday that the city hopes to hire police at the end of the year, but it will take another year to get the new recruits into the field.

New Haven Police Department Chief Frank Limon said at the press conference that the cuts are going to increase the workload for police officers and the response time for some calls. DeStefano added after the conference that the amended budget proposal leaves police with fewer resources than he would like.

The proposed cuts come amid a recent spate of murders in the city, which has left 11 dead so far this year, compared to 13 in all of 2009. The police announced earlier this month the creation of the new Street Interdiction Unit, which is intended to gather street intelligence and target career criminals, and which will take patrol cops from every district for staffing. Capt. Joann Peterson said the shift would not decrease police resources in each district because the officers the districts would lose would be replenished by new recruits.

Another recent police tactic, called Operation Corridor, relies on police overtime for its personnel. Both of those operations may now be in jeopardy based on the proposed budget cuts.

NHPD officials have also long prided themselves on the department’s community-based policing, the best example of which they said was the involvement of local district police managers in the everyday lives of residents. But with district managers no longer allowed to attend monthly community management meetings, police are losing a tool Assistant Chief Stephanie Redding has described as “crucial.”

Along with the cuts to the police department, the Board of Education will not receive the $3 million funding increase proposed in the earlier version of the budget. The amended budget cuts $1.5 million from the schools’ budget by eliminating such items such as the Talented and Gifted Program, non-academic summer programs and athletics programs. Another $1.5 million in cuts would come from a change in the Board of Education custodial services.

“[The amended budget] preserves the core and focus of school change,” DeStefano said after Monday’s conference.

Among other changes, the amended budget would also increase parking meter fees from $1.25 to $1.50 and building permit fees from $25 to $27.

Still, Harry David, a member of the NHCAN steering committee, said the amendments are not enough.

“These are really scratching the surface,” David said, adding there are not enough structural changes.

NHCAN circulated a petition advocating 10 percent cuts across city departments, which would result in no tax hikes.

“It’s a matter of perspective in tough times,” DeStefano said. “That’s why I feel relatively comfortable taking this package and asking taxpayers to spend $18 more a month.”

The Board of Aldermen is scheduled to vote on the budget on May 27.