Police would not say if alcohol was a factor in the alleged offending.
Lauaki and Cocker were both remanded on bail after their first court appearance last Wednesday. Lauaki is to appear again this morning and Cocker 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.
When an officer is charged with a criminal offence, such as wilful damage, he or she is also subject to an internal investigation and disciplinary action.
Cocker was not on duty at the time of the alleged offending, but his conduct will still be scrutinised by police bosses and a conviction could end his career in law enforcement.
When contacted yesterday Cocker said he could not comment "at this stage" and referred the Herald to his lawyer, who said she had "no authority to comment on his behalf".
He is based in the Auckland City district and works in the Mt Wellington area, where he grew up.
He has played rugby for the New Zealand Police tournament team and is a well-known amateur boxer who has competed in charity fights.
Lauaki, who played 17 tests for the All Blacks, scoring three tries, did not respond to messages yesterday.
The Tongan-born loose forward also played Super Rugby for the Chiefs before moving to France to play for Bayonne.
In January 2012 his health rather than his rugby put him in the spotlight after a routine biological assessment showed up heart and kidney problems. It also ended his playing career in France.
"What has happened to me is disappointing. I've never had these types of problems before but that's life, and it's necessary for me to look after myself," Lauaki told French newspaper L'Equipe at the time.
Former agent Bruce Sharrock said he was unaware of the charge against Lauaki.
"Sione has not played professional rugby for over 18 months. Given this I no longer represent him," he said.
