Crawford, who now coaches the Los Angeles Kings, could be liable for millions if a judge decides Moore deserves compensation for his injury.
Moore originally filed the suit against Bertuzzi and the Canucks, seeking up to $38 million. Court documents now show that Moore has consented to naming Crawford as a third party in the case.
Bertuzzi sought to have Crawford included, saying his NHL contract compelled him take orders from his coach.
"It was a term and condition of Bertuzzi's employment with the Vancouver hockey club that he was to take direction from Crawford in all matters related to his role or function as a player," court documents state.
Bertuzzi alleges Crawford urged him and his teammates during a March 2004 game against the Colorado Avalanche "to make [Moore] 'pay the price' " for a hit against Vancouver captain Markus Naslund two weeks earlier.
Bertuzzi's lawyer, Geoff Adair, would not comment on the latest development in the case.
"We are not prepared to comment on matters before the court," he said. "We strongly believe the fair and right thing to do is let the process play out in the courts."
Bertuzzi stalked Moore from behind and tugged on the back of his jersey before sucker-punching him in the side of the head and driving his body to the ice during the 2004 game.
Moore was bleeding from his face as he was taken off the ice on a stretcher. He suffered a concussion and three fractured vertebrae in his neck and hasn't played hockey since.
Bertuzzi, who now plays for the Anaheim Ducks, was suspended by the NHL and charged with assault causing bodily harm in June 2004 after a four-month investigation. He pleaded guilty, received a conditional discharge and was sentenced to probation and community service.