MPelletier が述べたように、2 組の DateTime が必要です。
var start1 = new DateTime(2013, 4, 10).Ticks;
var end1 = new DateTime(2013, 4, 20).Ticks;
var start2 = new DateTime(2013, 4, 9).Ticks;
var end2 = new DateTime(2013, 4, 11).Ticks;
if (start2 < end1)
{
//// Overlapping
}