Do I need to provide a police certificate with my application for permanent residence?

Yes.

National Bureau of Investigations (NBI) Clearance Certificate printed on green paper before January 2018, or Multi-Purpose Clearance Certificate printed on blue paper since October 2017.

If you do not live in the Philippines:

Complete an NBI Clearance form no. 5 application (available at the Embassy/Consulate or on the National Bureau of Investigation website). Write on your application why you need the NBI Clearance certificate (i.e. Immigration purposes)
Complete a fingerprint form (available online or at the Philippine Embassy/Consulate) and have your fingerprints taken by a recognized police or law enforcement agency where you live. The person taking your fingerprints must sign the form.
One 2×2 inch picture with a white background (taken within the past three months)
A photocopy of your passport
A photocopy of your Identification Cards
Applicable fees (Check with the issuing authority for rates and payment instructions)
Your authorization designating a family member or representative to act on your behalf (if applicable)

Source:

How to get a police certificate – Philippines