All IIT asks for a standard medical test during admission. IIT Bhubaneswar is no exception and everyone needs to do a medical test in order to get into this IIT. It is clearly mentioned in annexure IV of IIT Bhubaneswar. It’s a standard procedure, so there is nothing to worry about. The authorities will ask for your medical report during your counseling.
You can get the test done back in your city. There are also options for doing the medical test in Bhubaneswar. Just take the printout of the format provided by the institute and go to the nearest government hospital. In general, they will provide all the reports within 3 or 4 days after. If you are lucky you may even get the reports the very next day. But it should be a hospital impaneled by the institute. To stay on the safe side, it’s better to do the test at your home itself and make the registration process easy.