Hi Rabindra !

A candidate having the domicile of a state cannot apply for the central counselling of that state. He/she has to participate in the state counselling only given that he she has a domicile of that state but in case if he /she does not have the domicile then the candidate can only participate in Central counselling .

But since the centre counselling starts before the state counselling if you participate in all India counselling  in first round  , you can participate in state counselling also .  But if you participate in second round also , you cannot participate in state counselling .

So , yes you can apply for both the counsellings but not simlutaneously since state counselling starts only after the end of central counselling.

To know more about the counselling process of NEET ,do follow the given link:

https://medicine.careers360.com/articles/neet-counselling