A loose or leaking showerhead is almost always a thread seal issue. Plumber's tape and five minutes is all it takes.
Turn the showerhead counterclockwise by hand. If tight, wrap a cloth around the fitting and use an adjustable wrench. Wipe the exposed threads on the shower arm clean and remove any old tape or mineral buildup.
Wrap PTFE plumber's tape clockwise around the shower arm threads — the same direction you'll be tightening. Apply two to three layers, pulling the tape snug as you wrap.
Screw the showerhead back on by hand until snug. Wrap a cloth around the fitting and use the wrench for a final quarter to half turn. Turn on the shower and check around the connection for drips.