Paid VAT two times can I get back the extra money back

i Purchased a car from kerala. and i registered it in tamilnadu. so i paid entry tax. actually entry tax include VAT. but i already paid VAT at the time of purchase. so my entry tax must be reduction of this VAT amount right? i asked commercial tax officers in some other region about this they confirmed this. but in my region they never accept this. and they told me to pay full VAT(nearly 78000). so i paid that by DD. VAT is under central Govt right? why i want to pay VAT in two pleases? can i get that extra amount back? please tell me the legal move i want to do.