Hi there,
Earlier i had also gotten my PCC from local district police station. When i took it to my agent, he refused that and asked me to get one from the PSK instead. PSK procedure is quite straight forward and I got the PCC in one week - this duration also depends upon where you are staying.
If your medical is passed then most probably a program assistant has gone through your application, and even after that if you haven't heard from them regarding PCC - I
guess and hope PCC from Police station is fine (choosing my words very carefully here)
You must have gone through this link
https://www.canada.ca/en/immigration-refugees-citizenship/services/application/medical-police/police-certificates/how/india.html. It does mention something about getting PCC from local district police station.
Just have the PCC from PSK ready with you nonetheless. And submit that too, through CSE.