Sixty-one asymptomatic staff at Ninewells Hospital have been tested after a departmental outbreak.
An investigation was launched after a number of people tested positive in a non-Covid ward in mid-April.
Six of those tested were found to be positive but it is not known how many went on to develop symptoms.
It comes as fears grow transmissions may come from those who show no signs at all of illness.
Scotland’s national clinical director, Jason Leitch, recently said asymptomatic spreading is “unusual” but can happen.
NHS Tayside have not shed any light on whether the outbreak spread from one of the asymptomatic staff members.
A spokesperson said: “Across Tayside, as in all health boards, there have been positive cases of Covid-19 identified in some areas which are non-Covid wards.
“When this happens, the Infection Prevention and Control Team ensures that all appropriate measures are in place for patients and for staff.
“There is also a very active Covid-19 testing programme for patients and staff to identify cases as quickly as possible and ensure that all measures are being taken by our clinical teams.
“As the public would expect given the current pandemic, infection control measures in our hospitals are extremely prominent and remain at the forefront of everything our staff are doing.
“The use of personal protective equipment (PPE) is also being monitored constantly and is being appropriately deployed across all areas with clear guidance for all staff on what to wear in different situations.”
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