As per Section 22. (1) Every supplier shall be liable to be registered under this Act in the State or Union territory, other than special category States, from where he makes a taxable supply of goods or services or both, if his aggregate turnover in a financial year exceeds twenty lakh rupees:
Also as per Section 23. (1) The following persons shall not be liable to registration, namely:––
(a) any person engaged exclusively in the business of supplying goods or services or both that are not liable to tax or wholly exempt from tax under this Act or under the Integrated Goods and Services Tax Act;
After considering above points, in my view registration is required but only in that states from where taxable supply is made.
this is my personal opinion before relying on it kindly take opinion of professional too.