Officers conducting a routine patrol at Ermington at 3:45am on Thursday became suspicious about a white BMW that appeared to have been dumped.

Thirty minutes later, police stopped a taxi in the same street. The male and female passengers jumped out and fled.

The 31-year-old man was able to evade police, run to the nearby Parramatta River and dive in.

Fifty minutes later, water police found the man's body about 1.5 kilometres east of where he had jumped in.

The woman was arrested a short distance from the taxi.

Acting Assistant Commissioner David Eardley said the man was known to police but would not divulge any more information as his family had not yet been notified of his death.

He also would not say why the BMW had raised police suspicions or whether it was stolen.

The event is now the subject of a critical incident investigation.

"Any time you have someone who loses their life over something so meaningless is always a tragedy," Acting Assistant Commissioner Eardley said.

"This is also very traumatic for the police involved. You have police who are out proactively patrolling, trying to prevent incidents, and you have a situation where they have come across some type of activity in their duties.

"The circumstances of this incident, both leading up to it and during it, will now be investigated."

He said while the critical incident was in its infancy, there was nothing to suggest police had acted inappropriately.