Bigamy and divorce

Marrying again during lifetime of spouse or wife: Whoever, having a husband or wife living, weds regardless in which such marriage is void by reason of its occurring during the existence of such husband or wife. This provision doesn't stretch out to any individual whose marriage with such spouse has been announce void by a Court, nor to any individual who gets a marriage during the existence of a previous husband or wife, if such husband or wife, at the time of the such marriage, have been ceaselessly missing from such person for the space of seven years, and will not have been known about by such individual as being alive inside that time gave the individual contracting such resulting marriage will, before such marriage happens, educate the individual with whom such marriage is contracted of the genuine condition of realities so particularly far as the equivalent are inside their insight.
Bigamy shall not apply if: 
•    the first spouse is dead
•    the first marriage has been confirmed to be void by a Court with jurisdiction in the matter 
•    the first marriage has been ended by divorce
•    the first spouse has been missing or absent constantly for a space of 7 years.
The Supreme Court has held that while lodging such complaint, it is not necessary for the aggrieved party to prove the authenticity of the marriage as it is for the Court to decide the veracity of the allegations
Complaint for cheating (section 415) can be filed under the Indian Penal Code in case the person hides the fact of first marriage.
To prove the offence of bigamy, there should be sufficient evidence to prove they have contacted second marriage without abolishing the first one.
The divorce procedure in India is divided into the following stages:
•    Filing of the petition
•    Service of summons
•    Response
•    Trial
•    Interim orders
•    Final orders
Hence, a mere letter head cannot be conclusive evidence for divorce and can be challenged. 
 

Divorce by the process of law decided by the judgment in competent court of law is only valid.  Consent of divorce written on any letter head etc. is not a valid divorce but it can be filed as evidence in the court of law.  In case the police officials are closing your FIR or not taking an action, there are other legal remedies enshrined in the criminal law.