Does my state refund pay the tax owed to the federal tax due? If not why was my state return reduced by what is owed to the Fed.?

Nope...never...They are entirely different tax systems and operate (mosly) independent systems.

Nor could you have a FED refund and direct it to the state

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One of the review pages show an "effective" refund...but that is just a summary (and a bit "overhelpful" ) 

That's my dilemma too,  I owe Federal tax and I e-filed my Federal due and already accepted and amount owed will be pulled my checking account  on 04/01/2021.   

However,  when I am about to e-file my  State refund  Turbo Deluxe showed that my State Refund will be  reduced by my Federal tax due amount even   the amount owing  is scheduled to be pulled from my checking on 04/01/2021.

So, if that's the case the Federal tax due will be paid/pulled twice .  I decided not to e-file my State Refund, will just mail it to make sure my refund will not be reduced. 

@mambata1200 

DON'T Mail it in...go back and e-file it.   Mailed-in tax returns can take months to get processed.....  IF you are uncomfortable anyhow, just wait until (say) 10 April, and e-file the state tax return then

A State refund will NEVER be automatically directed to pay the Federal balance due.  There is absolutely no way to set that up to be done, and will NOT  be done automatically.