No.

There is no need to apply separately as for state and private colleges counseling will be centralized, conducted by particular state and the registration process will be online and single and it will be the same for AIQ, deemed/central  universities  as well.

For reference, you can go through the below article -

NEET 2018 Counseling

You can check the previous year counseling portal for the same below -

http://www.mcc.nic.in/

Good Luck!!!!