Here is a sample template you can use to write an authorization letter for a birth certificate.
To Whomsoever It May Concern
This letter is to bring to your notice that I, hereby authorize [Name] to act on the matters concerning my birth certificate. I grant [him/her] the authority to manage all the related concerns and take necessary actions.
I request you to consider the effect of [his/her] actions including official signatures equivalent to my own until further notice. I have provided the mentioned applicant with the necessary details and request you to cooperate with the same.
Kindly, make note of the mentioned concern and feel free to contact me at [Phone number], for further clarifications.