One must remember that rarely women have become pregnant after tubal ligation. It is estimated that about 1 in 200 women have had pregnancy after their tubes are ligated. This may be caused by an incomplete closure of the tubes.
Complications due to
anesthesia are rare and include:

Reactions to Anesthetic medications

Breathing difficulties
Complications of
surgery are rare, however these include -

Bleeding

Infection

Damage to the bladder

Puncture (perforation) of the uterus

Laceration (tear) of the cervix.

Perforation of the fallopian tube.

Perforation of major vessels - laparoscopy

Cardiac arrhythmias – due to CO2 - laparoscopy

If pregnancy occurs after the procedure, there is an increased risk for an ectopic pregnancy in which the pregnancy develops in the fallopian tubes.