Kansas City, Mo. ? When voters approved a sales tax increase more than two years ago, city officials promised to use the money to add 20 police officers a year to the Kansas City Police Department.

That would have meant 60 new officers by now, but so far, only five have been added to the force of about 1,300. In spite of the tax revenue, the department said it didn’t have the money to hire more officers.

“We have 55 vacancies,” Maj. Christine Laughlin said. “We can’t fill any of those for budget reasons.”

The city has given the department money to pay the salaries of 60 additional officers, but it underfunded by $6 million other parts of the police budget, including health insurance and workers’ compensation. The department said it had to use some of the money intended for hiring more officers to fill the budget gap.

The situation could get tighter this year, with the city facing a potential funding shortfall of $16 million to $29 million. At the same time, the department is getting ready to open a new police station that will create a need for more personnel.

The budget crunch comes at a time when police response times, termed “totally unacceptable” by department officials four years ago, have worsened.

“The less officers you have on the street, the more likely they will be running from call to call to call instead of having time to get to the root causes of problems,” said Chief Jim Corwin, who took over the department in October. “Less officers cuts time devoted to follow-up, checking whether a certain crime is part of a pattern and figuring out why this is happening in a neighborhood. It’s all linked back to manpower.”

Department officials have been trying to add to the police staff for at least a decade. In 1993, voters rejected a tax package that would have included money for 120 new officers.

The response-time report issued in 2000 showed officers averaged more than 10 minutes to respond to the most urgent 911 calls, including rapes in progress, shootings and stabbings. A sales tax package put before voters in April 2002 was only for capital improvements projects in the police department, but the city promised to hire 20 more officers a year for nine years if the package was approved.

In November 2004, the average response time in four of the city’s police districts was more than 15 minutes.

Troy Schulte, the city budget director, said he thought the department could add the promised new positions if it found other ways to save money, perhaps by reducing the number of civilian employees and commanders.