["way of management"], late 14c., policie, "study or practice of government; good government;" from Old French policie (14c.) "political organization, civil administration," from Late Latin politia "the state, civil administration," from Greek politeia "state, administration, government, citizenship," from politēs "citizen," from polis "city, state" (see polis).
From early 15c. as "an organized state, organized or established system of government or administration of a state," but this sense has gone with polity. Also from early 15c. as "object or course of conduct, or the principles to be observed in conduct," and thus "prudence or wisdom in action" generally, but especially "the system of measures or the line of conduct which a ruler, minister, government, or party adopts as best for the interests of the country in domestic or foreign affairs."
["written insurance agreement"], 1560s, "written contract to pay a certain sum on certain contingencies," from French police "contract, bill of lading" (late 14c.), from Italian polizza "written evidence of a transaction, note, bill, ticket, lottery ticket," from Old Italian poliza, which, according to OED, is from Medieval Latin apodissa "receipt for money," from Greek apodexis "proof, declaration," from apo- "off" + deiknynai "to show," cognate with Latin dicere "to say, speak" (from PIE root *deik- "to show," also "pronounce solemnly"). Also formerly a form of gambling, "the numbers game" (by 1830).