For federal income tax purposes you should file as single. Under federal tax law you determine whether you're married or single on the last day of the year, and that determination applies for the entire year. The IRS has a publication that discusses many of these issues - Publication 17 - the relevant part of which you can review online here: http://www.irs.gov/publications/p17/ch02.html
So, even though you were married for all but 24 days of 2012, because you were divorced on December 31, 2012, the IRS considers you to have been single for all of 2012.
I do not know if you would have a different filing status for the purposes of Kentucky state law, so you should check with the relevant state tax publications, or contact the Kentucky tax agency directly if it's not clear from their publications or the instructions on their tax forms.
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You will have to file according to your marital status at the end of the year (12/31/2012). Accordingly, if you were not married on that date, your filing status will be single.
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the date to focus on is 12.31.2012, if you were single then, you must file single. take care.
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