Absolutely you can !
According to Indian Supreme Court, there's no specific rule that can prohibit one person from giving two same examinations . If you want to qualify for your boards from two different states, please try to register with a minimum 1 year gap.
It is also mentioned in Indian Law, that is if a student is caught appearing for two exams in the same year, he/she can be suspended from appearing in any type of exam for atleast next 3 years.
So be careful.