These local cops are city employees. The police guarding the hospice are employed by the city of Pinellas Park. I've noticed a couple Sheriff's, they are employed by the county.
Each municipality in Pinellas has it's own police force. The Sheriffs oversee unincorporated areas, and assist local police forces.
Every municipality in my county has a police force, too. It doesn't matter -- if one party runs the county, then the politicians can exert influence across municipal lines. My closest friends's father just retired as borough council chief of his town. I've seen him threaten cops (in my presence) in other towns with firing if they didn't immediately obey his wishes (like taking a pregnant mother to the bathroom while her husband took wedding pictures with his son). All he would have had to do would be to place a call to his buddy in the cop's town.
Make no mistake, all the local politicians know and support each other (believe me, I know -- my uncle is an elected politician and he once mentioned that he can fix any local ticket because he knew all the judges). Local cops disobey them at their peril.