No, writing NEET is not required to get admission in forensic sciences. Colleges and Universities conduct their own entrance exam for admission in a forensic science course. So you need to stay updated about the entrance exam of the colleges that you are targetting for. I'm attaching a link below which has a list of good colleges for forensic science in India. I hope it will help you.

https://collegedunia.com/courses/bachelor-of-science-bsc-forensic-sciences-colleges-in-india