Hi Bikramjit, 

Yes, of course as a government employee you can pursue higher studies in distance mode from a distance education center. However, I strongly suggest that you consult your reporting manager/senior before enrolling as you will have to take leaves to appear for exams. It is important to seek permission from your department, but it should not be a problem.  

IGNOU ( Indra Gandhi National open university) is offering a special course called distance and e-learning programmes for govt. employees (DELPGE) which are free of cost. There are approx 140 courses provided by the university. Check the university site for more info.