Does this state park have public showers for the campers?

Its not a park its a forest with lots of trees there are individual places to camp but not in capitol state forest it self per se they are off down mima rd and the only one I know of is Margaret McKinney campground and no they don't have any running water

No, I don't know of any state forest land that have showers or any services other than pit toilet and some times dump station.