Police had issued an arrest warrant for a suspect three weeks before he stabbed to death his ex-wife.
Leon McCaskre, 41, was wanted for allegedly breaching a stalking restraint order and not turning up for a court hearing.
On Monday he attacked his ex-wife Yasmin Chkaifi, 43, stabbing her multiple times in a west London street, before a motorist drove into and killed him in an apparent attempt to stop the attack.
It is thought she might have been hit by the car, too.
The Metropolitan Police has referred itself to the police watchdog because of its previous contact with Ms Chkaifi.
The Independent Office for Police Complaints has been asked to investigate the force’s previous contact with Ms Chkaifi to see if it could have done more to protect her.
The driver of the car, 26, was arrested on suspicion of murder and later bailed.
Some witnesses said he was among those who tried to help the woman but were threatened by the knifeman in Maida Vale at 9am on Monday.
He is then said to have got back into his car and appeared to use it to drive at the knifeman to try to stop the attack.
Ms Chkaifi’s family reportedly hailed the car driver as “our hero.”
The IOPC must now decide whether to investigate, ask the Metropolitan Police to investigate internally or take no further action.
The IOPC said: “We can confirm that we have received a referral from the Metropolitan Police regarding their contact with Yasmin Chkaifi prior to her tragic death in Maida Vale, London on 24 January.
“We are currently assessing the available information, and have requested more, to determine what further action may be required from us.”