You should have applied for NoC at the time of applying for the State Government job. Now, you can't apply for the same. You have to tender proper resignation and join the State Government service. I strongly advise you not to abscond from your present job, which many people would advise under the present circumstances.
You should submit a detailed application explaining the position to your present office and should state about your ignorance of procedure. Stating the circumstances, you should apply for technical resignation. If the organisation allows your application for technical resignation, your present service will be counted with your next service in State Government for the purpose of counting service for pension. You will get some other minor benefits also.
If your present office does not accept your application for technical resignation, then you can tender your resignation and join the State Government. In that case, your present service will not be counted with your future service, but you will not be treated as an absconder.
I reiterate not to abscond from your present post and advise you to submit application for technical resignation.
Beware! I question everything and everybody.