That is what the Washington Times is reporting this morning. "NASHVILLE, TN, January 9, 2014 – According to official
state voter roll calls, Senator Lamar Alexander (R-Tenn.) voted in the
2012 Tennessee Democratic Primary." (link) If that is correct, that is very strange. Even Democrats didn't vote in the Democrat primary in 2012. That was the year that the nomination for senator was won by nut-job Mark E. Clayton in a field of unknowns.
Update: Apparently that was false story. According to the Tennessean, the Blount County Election Administrator says Alexander voted in the Republican primary and the Washington Times has withdraw the story. (link)