PSNI chief constable Simon Byrne sent an email asking for officers to be "thinned out where possible" and for officers to be "sent home in rotation" during the coronavirus pandemic, it has been reported.
An internal inquiry was launched last week after it emerged that dozens of officers did not report for duty in Londonderry and Strabane during a two-week period in April.
It is understood that on one shift as many as 28 officers did not show up for work.
The PSNI said that, once discovered, the practice was brought to "an immediate end" and an investigation was launched into the matter.
The force acknowledged the situation would have reduced the enforcement of lockdown restrictions.
Chief Superintendent Emma Bond last week said that the practice "is not one that had been endorsed by the senior management of police."
However, an email sent from PSNI chief constable Simon Byrne's email address, seen by BBC Radio Ulster's Nolan Show, asks for "numbers to be thinned down where possible" and approved officers being sent home "in rotation".
A PSNI spokesperson said it would be "inappropriate" to comment on the matter while an internal investigation is under way.
Former PSNI assistant chief constable Alan McQuillan, speaking to the Nolan Show, said it was an "very odd sequence of events".
"I think it just reflects the confusion there was at the start of the pandemic," he said.
"I heard that message was sent out by the chief constable. There was also some public messaging going on from the government at that time about self-isolation."
Mr McQuillan said there may have been some confusion within the force about sending home staff who had come in contact with people who had Covid-19 after the government issued advice that these people should self-isolated for 14 days.
"That instruction went out and things were interpreted at local level," he said.
"What I really don't understand is why suddenly at the Policing Board there is an announcement that there is an investigation, an inquiry into this.
"Which almost makes it appear as though there has been some sort of malpractice. I just don't see that. There may have been a break down in communication, there may have been some misunderstandings but it seems to have gathered an entire life of its own for no reason."