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Lauaki, 32, a former All Black loose forward, entered the plea through a duty lawyer at Auckland District Court this morning.
He was remanded on bail until his next appearance in February.
A police officer was suspended from duty after he was charged alongside Lauaki.
Police allege Constable Takao Cocker, 31, and Lauaki intentionally damaged a taxi about 3.30am at Greenwoods Corner, Epsom on December 13.
Court documents revealed Lauaki allegedly damaged the vehicle's CCTV camera and Cocker damaged a wing mirror.
Lauaki and Cocker were both remanded on bail after their first court appearance last Wednesday.
Cocker is due to reappear again on February 4.
Auckland police spokeswoman Noreen Hegarty said Cocker was stood down from police duties on full pay just hours after the alleged incident. As the matter was before the courts, police could not comment further.