Succession certificate or Inventory or letters of admin required?

My father passed away in Mumbai in 2009. He had bought a property in Goa in 1999 and had built a house on it. He didnt leave a will. So after his death my mother, my elder sister and me would be the legal heir to claim this property in Goa? What is the process to claim the property? We all are born and brought up in Mumbai and hence all the documents are of Mumbai. Do we have to obtain the certificates from Mumbai or in Goa Court? Do we have to obtain succession certificate or legal heir certificate or letters of administration for acquiring this property? What would be the procedure for obtaining these documents and how much would be the cost approximately for it and also the time. I have been informed that the entire process would take around 6 to 7 months and charges would be Rs 15000 for obtaining succession certificate in Mumbai and court fees would be max Rs 75000 as after property valuation we would have to submit it as the value of the property at current stage. after obtaining this succession certificate we would have to submit it in Goa mutation department. I asked the mutation officer in Goa and i was informed by the officer that either Inventory or Succession certificate has to be submitted here without which there would be no document transferred on my mother's and sister and my name. Is it correct or the information provided to me is wrong? Kindly let me know