No, a state police officer is not considered a Fee-basis state or local government official.
"A fee-basis public official receives and retains remuneration directly from the public".
For reference, please click here: https://secure.ssa.gov/poms.nsf/lnx/1960001625.
Form 2106 Instructions: https://www.irs.gov/pub/irs-pdf/i2106.pdf.
