This is possible if you have credits such as the Child Tax Credit, Earned Income Tax Credit, education credit, or any of the other many credits reported on Schedule 3 available to you.  

I reviewed my printed Federal and State Tax forms as well as my input into Turbo Tax.  I qualify for the standard deduction and I do not qualify for any of the credits you referenced (nor did I input data for credits or were forms printed out).  My income comes from a Partnership Schedule K and it appears that my income is computed correctly for Federal and State purposes.  

My Federal Return computes an AGI of $34,450 and no Federal Income Tax due.  However, my State Return uses my Federal data and appears to calculate a state tax obligation.

What am I doing wrong?

Think I figured it out .... it is the composition of my income that drives the answer.

MY AGI was $46,865.  Of this, $38,555 was Long-term Capital Gains.  I believe my income level falls below threshold for taxing my Long-term Capital Gains.  They are then excluded from the tax calculation.

What is confusing is that Form 1040 Shows my taxable income as $34,470.  Yet, it would appear that the number used to compute my tax due is much lower that that after adjusting out the Long-term Capital Gains.

Can you confirm my thoughts as to what has happened?

Yes that is correct.  There is a worksheet called the Qualified Dividend and Capital Gain Worksheet  (Qual Div/Cap Gn) that provides the calculation.  It does not show clearly on the 1040.