Can I go back and change the return I already filed my tax return claiming my son as my dependent but I've decided to let his father claim him because my son resided with his father last year?

Generally, yes. Form 1040X is Amended U.S. Individual Income Tax Return. To change the number of exemptions (personal and dependent) claimed on your original return, you fill out lines 25 to 32 in Part I-Exemptions on page 2 of Form 1040X.

There is a special situation for a Qualifying Child of more than one person. You both can have a tax benefit. The noncustodial parent can claim an exemption and the Child Tax Credit for the child. The custodial parent can claim the child as a Qualifying Child for (1) Head of Household filing status, (2) Credit for Child and Dependent Care expenses, and (3) Earned Income Credit.