See TNPSC organizes examination for different job profiles like Administration, State Technical post, Police service etc. Now if you want to go for any examination which needs a eligibility criteria of Graduation then you are definitely eligible for the examination.

Now as you are from the law background then you can also apply for Tamil Nadu Judicial Service through which you can get entry to judiciary in lower benches which is also a Government job. SO you should be very keen about what you go for and depending on your interest you should attempt and prepare for the examination.

I hope this answer helps. All the very best for your future endeavors!