Apply to and Go to your nearest Passport Seva Kendra in Delhi.
If your address in passport is different, take an address proof (like Gas Book, with latest bills, electricity bills etc) which are in your name.
At max they'll ask you to do a physical police verification, so do it, it's not a big deal (unless you're worried about the "charges" you might need to pay to police).
I have the same case in Bangalore, my passport's address is of UP and I live in Bangalore since last 6+ years.
I got the PCC right there, no physical verification was required and the whole process took less than 2.5 hours.
I applied after getting the ITA