The general election is Nov. 5.
Munson said consolidating the Washington County Sheriff's Department with the Hagerstown Police Department would save both jurisdictions management costs and strengthen patrol coverage.
"Call it a sheriff or a chief ... it would save in management," Munson said.
"I am always willing to listen to any possibilities," Swartz said.
Swartz said discussions to combine any county or city departments might hit stumbling blocks because of employee unions.
Nipps, a member of the Washington County Board of Education, said the police departments and the county's fire and rescue companies need to get past "turf battles" and decide what the needs of the county are.
Hardin, also a School Board member, made similar statements.
"We have to have these people at the table discussing what the options are, because we will have to be a city/county government," Hardin said.
Wivell said the city and county may want to look into combining patrol services.
The remaining five candidates didn't oppose looking into a combined police department, but they offered additional ways the county and city could save money.
Kercheval and Cramer supported studying the merits of a central booking facility. Wivell said he wasn't opposed to central booking but that it would require cooperation from the county, city, state and other agencies.
Brown said a committee should be formed to determine whether consolidations of any type are feasible. If so, he said combining the permits and inspections departments of the city and county to create a "one-stop shop" might save money.
Iseminger and Snook said the city and county have already combined some services, such as sharing bids and purchasing expenses, but other options remain.
Iseminger said consolidating the human resources departments might save money, while Snook said consolidating the parks and recreation departments is an option.