Both Givens and Mayor Charles F. "Skip" Kauffman Jr., said the matter has not caused a major problem, but that town officials want changes in the way the three deputies are deployed.
The town pays the sheriff's office for three deputies who patrol the community. A federal grant pays part of the salary for one of the deputies.
The most recent concern has been a lack of communication among the deputies, town officials said. Kauffman said the deputies have not had enough opportunity to speak to one another because there is not enough overlap in their schedules.
"We want them to overlap so they can communicate better," he said.
First Sgt. Doug Mullendore the deputies, themselves, should solve any communication problem.
"That sounds like a problem that needs to be addressed separately," he said.
Mullendore said the department listens to town officials' concerns. For instance, patrolling near the schools in the morning and afternoon is a priority, he said. For the most part, though, he said the department aims to cover the greatest number of hours.
"The more overlap you get - two people working a small town - that's not the best use of resources," he said.
Sometimes, however, the problem is too much overlap, Givens said. A couple days last week, he said, two of the deputies have worked 8 a.m. to 4 p.m. shifts while the third deputy was on vacation.
The goal is to find a happy medium, Givens said.
"That's what this meeting is going to be all about," he said.