If you are unable to use your ATM card on your own, here is a sample template you can use to write an ATM card authorization letter.
The Branch Manager
This letter is to inform you that I am [Name], and I hold a [savings/credit] account in your bank. My account number is [Account no.] and I have an ATM card (Card no.) issued to me as well. Due to [reason], I am unable to operate my ATM card on my own.
This is why I want to authorize my [son/wife/etc.], [Name] to operate it for me until further notice. I have provided [him/her] with the card details and I request your cooperation for the same. Kindly contact me on [Phone number], in case of any further clarification.