I made a traditional IRA contribution of 5,500, it lowered my state tax due, but not my federal tax due. Can anyone explain to me why?

[DawnC0]

Your deduction is probably limited or disallowed on your federal return and not limited on your state return.  Each state has its own rules regarding tax deductions.  Your IRA contributions are limited on federal return as follows:  

For 2018 - 

• IRA Deduction if You ARE Covered by a Retirement Plan at Work - 2018
• IRA Deduction if You Are NOT Covered by a Retirement Plan at Work - 2018 (deduction is limited only if your spouse IS covered by a retirement plan)

[Ivysun]

But turbo tax showed that I am allowed the IRA deduction under the federal return.

[DawnC0]

Maybe you got a bigger deduction on the state return.  The deduction amounts are not the same for federal and state.  The links above are for the federal deduction.  And although you may be allowed a deduction - it may be limited.  You will need to look at your tax return to see the exact amount of the deduction.  See Schedule 1 - Line 32