Hello Kaniknath , Yes you can surely go for Law corse by Distance Education while you are workinng in the services of Indian Government but you can not appear in the court  ,  for dosing so you gonna need the license issued by the Bar Councillor of India and that wouldn't be issued since you are an employee under Governemnt .So if you want to ptractice the Law , you will have to quuit the Government job.

Good Luck !!!