Yes, it is possible.
You can give improvement exam from any city of any state.
I will tell you my story:-
I gave first attempt of class 12th from CBSE board in Ratlam, (M.P.). I scored 78% in it. Then I decided to prepare for JEE and so I came to Kota and joined coaching institute. Here I get to know that my class 12th percentage are very less, due to which I will be unable to fetch a good rank. Thus, then I decided to give improvement exam.
I had done all formalities that are required to give exam. I gave class 12th exam from Kota (Rajathan) so that my improvement exam does not affect my preparations for JEE. I scored 89% in my second attempt which finally enables me to get NIT.