what does your training involve?
If I do 3 sets of chins in the morning then do squats at night does that equal 2 sessions per day? I don't think so, but you might.
What program are you following that has you training morning and night?
I see overtraining as overloading the bodys ability to recover.
I don't see how doing chins/bicep curls in the morning would put you out for the day.
however, if you do an arse busting session of squats in the morning, I doubt you'd be doing deadlifts in the evening.
more details around your program would give a clear picture cause with the info provided it's very much a "how long is a piece of string" type scenario.