Here is a simple template you can use to write a key copy authorization letter.
(Company Name and Address)
Subject: Key Copy Authorization Letter
To Whomsoever It May Concern
I, (Your Name), a resident of (name of your area), would like to authorize (Authorized Name) for making a duplicate key of my residence. As I am traveling for a month and would not take care of my residence (Authorized Name) would do that in my absence.
I request you to provide him/her with the key copy of my residence.
(Your Name and Signature)