Can I use the free State that came with my CD to pay the $44.99 online? I have prepared my return online with Self-Employed instead of the Deluxe version I purchased.

Unfortunately, no, they are separate products.

You can get a refund for the CD product, however, if you didn't use it and are in the 60-day window.
<a rel="nofollow" target="_blank" href="https://support.turbotax.intuit.com/forms/refund-request.jsp">https://support.turbotax.intuit.com/forms/refund-request.jsp</a>

Or another option is to move (download) the *.tax2018 data file you started onilne to your computer and finish and file from your desktop software.  We can tell you how, but deadline is approaching.

So will the two versions "mesh" the information?

You have to download the *.tax2018 data file.  The *.tax2018 data file downloaded from an online account can be opened by any of the desktop software editions Deluxe and higher.  (Basic Edition can actually open it too, as long as there is no state return involved.)

If your *.tax2018 file has a state return in it,  you'll need to download your state program into your desktop software before opening the data file, or you'll get an error message.  If you haven't already downloaded your state program, then you may need to start a new fake return just long enough to download the state program before opening the data file.

It can't hurt to try, other than that the deadline to file is approaching.  You can still get a refund for the desktop software even if you have to go back and file it online.  But many people move from the online product to the desktop software.  There's even a FAQ, and here it is:

<a rel="nofollow" target="_blank" href="https://ttlc.intuit.com/questions/1901476-how-do-i-switch-from-turbotax-online-to-the-turbotax-software">https://ttlc.intuit.com/questions/1901476-how-do-i-switch-from-turbotax-online-to-the-turbotax-software</a>