Levy, from Tottenham, north London, was found guilty at the Old Bailey on Friday of two counts of murder, two counts of rape, grievous bodily harm with intent, and non-fatal suffocation.
He was remanded into custody ahead of sentencing on 12 August.
The IOPC later confirmed its investigation began in January following a voluntary conduct referral from the Metropolitan Police and remains ongoing.
It added that issuing misconduct or gross misconduct notices does not necessarily mean disciplinary proceedings will follow.
The watchdog is examining the management of Levy over a four-year period, from his first conviction in September 2021 on sexual assault charges up to his arrest in September 2025.
Levy had been released from prison on licence in February 2023 and was briefly returned to prison in May 2024 after being accused of rape and breaching his licence conditions but was not charged.
On Friday, he was convicted at the Old Bailey of two murders, rape and other charges including grievous bodily harm with intent, and non-fatal suffocation against the surviving woman.
The jury, which was given a majority direction in the trial, found him guilty on all counts.
During his trial jurors heard Levy had a string of convictions for attacking women dating back to July 2018, including one carried out against a prison officer in 2022.
An IOPC spokesperson said: “We are examining whether action could or should have been taken to prevent his reoffending, and if all officers involved in his management followed policies, procedures, and training.
“We are also assessing whether any learning, whether individual, force-wide, or nationally, or other changes should be implemented in light of the events under investigation.”