Can venipuncture cause carpal tunnel syndrome if done incorrectly?

Probably not: Veins that are used for blood tests or iv's are superfical to the carpal tunnel. Thus it is unlikely that a single needle stick would suddenly cause carpal tunnel. Hitting the nerve with a needle could cause a sharp pain or injury to the median nerve. A lot of bleeding from a missed IV or blood test may cause enough swelling to cause carpal tunnel, but this would require a large hematoma.

No: Carpal tunnel is a repetitive stress injury resulting in entrapment of the median nerve. An incorrect venipuncture won't cause this.