it is not possible to e-file a state return unless the Federal is also e-filed at the same time or earlier. could you have failed to select mail for the Federal return? had you selected mail for Federal you wouldn't be able to e-file state.
if you successfully e-filed the state you would have gotten an e-mail that said the state was accepted. did you get such an e-mail? if not, then it's almost a certainty they don't have it. call them to check.
all Turbotax could tell you was whether your returns were e-filed. it has no way of knowing if either or both were mailed. the IRS might be able to tell you if you filed two returns but only if both were entered into its system. with major delays in processing the IRS might only know about one return.
I wouldn't worry about filing two federal returns but I would worry that no state return was filed if you did not get a state acceptance letter.
