You cannot close your Demat account while maintaining your trading account. At least one Demat account must be linked to the trading account. Even if you don't trade, you'll need a Demat account:

As open intraday positions can go into delivery if they are not closed before the end of the day, equity intraday positions can go into delivery. These shares must be transferred to your Demat account.
Starting in October 2019, all Stock F&O contracts will be settled physically, requiring stocks to be settled to a Demat account in the case of taking delivery positions and debited from the Demat account in the case of granting delivery positions. More information on the physical settlement of stock F&O contracts can be found here.


Note: If you have numerous Demat accounts linked to your trading account, you can close all of them as long as you only have one Demat account linked to your trading account.