One can only file complaint, and the copy given by authorities is First Information Report. If you have already filed complaint, you are entitled to FIR copy as a right. Almost all police depts., have to place FIR in their website.
If you have not yet filed complaint, please file it immediately under copy to Supdt., of Police and wait for a month, and then file application seeking information on action taken on your complaint and also seek copy of FIR.
So you may pressurise the writ petition for an expeditious disposal through your advocate and wait for the outcome based on which further course of action can be decided.
Rightly advised by Learned Mr. Kalaiselvan, I agree with him. Mail your complaint addressed to the Commissioner of Police on-line and request him to treat the complaint as F.I.R for future reference.
You have already done what ever you can, but very very late. Now continue your efforts and enlist support of Womens' organisations that may help you, as they have seen several instances and are a collective force.
We can not do everything expecting positive results but certain basic formalities must be adhered to. If the matter appears before Court, all your efforts to avoid litigation and to get things in normal course are reflected in the correspondence. I do not know whether there is a scope for filing contempt petition for not commencing investigation, and whether there are any rules specifying the period within which investigation has to be completed in each case in your state. Some states have prescribed time frame.