In India only one state that gives the certificate is Punjab State.
But that state will give certificate to the people belonging to that state alone.
No other authority whether local administration or other authorities are empowered in law to issue such a certificate to the Indian citizen.
The laws of some countries require that, before a foreigner may marry within their jurisdiction, he/she must produce a certificate issued by the relevant authority of the country of which he/she is a national, stating that the authority does not know of any impediment to the marriage. However ministry of external affairs state that this certificate should be obtained from court.
Nomenclature of the certificate issued in India is generally called as 'No objection certificate' or bachelorhood certificate.
Since the power to declare any legal rights is vested in the competent courts in India, the applicant is advised to contact such concerned court authorities at the place of normal residence.