Mr Trump returned to the White House on Monday after being treated at the Walter Reed Medical Centre for Covid-19.
But staff with the Washington DC Department of Health have been unsuccessful in trying to connect with the White House and said it had not informed them of any positive results.
Mayor Muriel Bowser said: “We have reached out to the White House on a couple of different levels, a political level and a public health level.”
The lack of communication represents an unwelcome obstacle for the DC government, which has worked to contain the spread of the virus through mandatory mask requirements and limits on the size of gatherings.
Ms Bowser acknowledged on Monday that White House medical officials “have their hands full” at the moment.
But a DC official, speaking on condition of anonymity, said White House doctors have not informed the DC Department of Health of any of the positive test results – a necessary step before contact tracing and quarantining can begin.
There have been multiple attempts to contact them, the official said.
Ms Bowser’s government, which has publicly feuded with the Trump administration multiple times, is in a difficult position regarding the current outbreak.
The Trump White House has operated for months in open violation of several DC virus regulations, hosting multiple gatherings that exceeded the local 50-person limit and in which many participants did not wear masks.
A Rose Garden ceremony to announce Mr Trump’s nomination of Amy Coney Barrett for the Supreme Court is now regarded as a potential infection nexus, with multiple attendees, including Notre Dame University President Reverend John Jenkins, testing positive afterwards.
Reverend Jenkins flew in to attend the ceremony from Indiana, a state DC classifies as a virus hotspot – meaning he would have been expected to quarantine for two weeks upon arrival.
Washington’s local virus regulations do not apply on federal property, but the current outbreak has blurred those distinctions.
Mr Trump inner-circle members like former counsellor Kellyanne Conway, who has also tested positive, are DC residents, as are many of the staffers, employees, Secret Service members and journalists who have had close contact with infected officials.
But the Health Department has been unable to conduct contact tracing or any of the other normal protocols.
Instead it has been forced to entrust the White House medical staff to conduct its own contact tracing.
“There are established public health protocols at the White House that are federal in nature,” Ms Bowser said. “We assume that those protocols have been engaged.”
😷 Masks 😷 are not just for 🎃 Halloween 🎃 this year
Wear a 😷 mask 😷 today and every day#MaskUpDC— Muriel Bowser (@MurielBowser) October 3, 2020
The White House said Monday that it had a “robust” contact tracing program in place and procedures that follow Centres for Disease Control and Prevention specifications.
The situation has been further complicated by the apparent resistance of some senior Trump officials to voluntarily quarantine and the inability of the DC government to force the issue.
Attorney General William Barr, who was repeatedly seen in close contact with Conway and other infected people, said over the weekend that he would not limit his activities or movements.
On Monday he reversed course and a spokesman said Barr would self-quarantine “for now”.
