prefectural police (Osaka or Kyoto)
Refers specifically to the police force of Osaka or Kyoto Prefecture. Not used for other prefectures; those are called 県警 (kenkei).
府警が事件の捜査を始めた。
The prefectural police (of Osaka/Kyoto) began investigating the case.
京都府警は観光客の安全に力を入れている。
The Kyoto Prefectural Police are focusing on tourist safety.
The Osaka Prefectural Police are investigating the case.
I reported a suspicious person to the prefectural police.