Whether or not you have a CMB credit card will not affect your application for a CMB debit card. The same person can only open one Category I account (excluding credit cards) at the same bank, and the total number of card accounts opened by the same customer in the China Merchants Bank savings account shall not exceed 4.
(Response time: June 6, 2019. For the latest business changes, please refer to the official website of China Merchants Bank)