Did you file Joint last year? Do you know if you took the Standard Deduction or if you itemized deductions? If you took the Standard Deduction then the state refund is not taxable and your ex doesn't need it unless he needs it for something else.
Did you use Turbo Tax last Year? You have to log into that account. First LOG OUT of whatever TurboTax account you're logged into right now. Then use this TurboTax account recovery website to get a list of user ID's for an email address. Run the tool against any email addresses you may have used
https://myturbotax.intuit.com/account-recovery/
If you used the Desktop CD/Download program then the only copy is on your computer and not saved or stored online.
You can also request a transcript from the IRS
https://www.irs.gov/individuals/get-transcript
