Do I need to submit NOC or Relieving Certificate?

I am working for a government department, currently on probation. Before starting to work for the department, I had applied for another exam and attempted it before. But, I attended the interview after joining the department and was selected for job. I gave my current job details for the new employer, which is also a government department. Now, my question is will they ask for No Objection Certificate during joining from my current employer? Or is simply providing with relieving letter suffice? I have not informed my current department about my selection and I did not inform them that I was attending interview. My problem is this: If they want NOC, I have to do "technical resignation" for NOC and for that I had to inform the current department about the interview, which I didn't do. Or will I get NOC even after resigning on any other ground like family problem etc?