NO, dont do that (if you are presently in USA and completing the ITA from here). Do not complicate your case by adding something that is not the requirement. More over there is so much confusion over PCC from Indian police stations regarding formats, as different regions have their own formats.
If you are in India, then get PCC from PSK only, never from police stations cause of the format confusions. There are many rejections cause of incorrect PCCs from Indian police stations.
You need to send your FBI PCC and Indian PCC from Indian consulate, at the very least. You must only add PCC from other countries where you spent around 6 months or more. For these, follow the guidelines on country specific PCC as per the cic website.