It is not mandatory or compulsory to do so.. But if you do you get an extra edge over getting jobs since you have done masters in the same field and you've almost in depth knolwedge about the Forensic science course. Coming to your second question now, there are many top govt institutes recruiting forensic science aspirants in TNPSC. Some of them are - Junior Scientific officers, Government of Forensic Science Dept, Tamil Nadu.

Refer to the sites below for more detailed information..

https://university.careers360.com/articles/5326-Career-review-Forensic-Sciences

Best wishes. Thank you.