You can definitely change your 12th board. For both state and CBSE, NCRT text book is followed. The only difference will be the pattern of examination conducted. All the portions are same.

State board exam for 12th will be conducted by the state government was for CBSE it is conducted by cbse board.

The textbook followed is NCERT. Also for Neet examination the questions are from NCERT textbook. Hence it doesn't matter. Eligibility criteria for Neet examination is candidates must have passed their 12th from recognised board with subjects like Chemistry Physics and Biology. It doesn't focus on which board you studied. Hands you are completely eligible to give neat exam if you changed your board.

Thanks