Police use helicopters, but the etymology of helicopter has nothing to do with cops, but rather with fliers of the Jurassic period. It’s helico – pter, from the Greek ἕλικος (elikos) ‘spiral’ + πτερόν (pteron) ‘wing.’
In 1861 G. L. M. de Ponton obtained a British patent for and “aerostatical apparatus (which I intend denominating aeronef or helicoptere,) [which would ascend] by means of two or more superposed horizontal helixes combined together.”
ἕλικος is also the source of the word helix.
The -pter in helicopter is the same as the –pter in pterodactyl. The prehistoric flying reptile is “wing-fingered.” It gets its name from πτερόν + dactyl, the combining form of δάκτυλος (dactylos) ‘finger.’ In 1829 geologist Charles Lyell noted that Mary Anning had discovered a new “Pterodactyle of Lyme.”