Having brown discharge started 2 days ago im suppose to start my period in the next week or so but i had a tubal ligation?

A "brown discharge" is usually secondary to light bleeding, which may occur at mid-cycle ovulation if two eggs were released at ovulation, since the estrogen level was increased and the drop in estrogen prior to ovulation is enough to cause minor bleeding. "Tubal ligation" is usually close to 100% certain, but not "perfect". If your period is delayed, see your GYN physician for guidance.