Government figures show there have been 313 cases in the borough - two more than last week.
York Teaching Hospital NHS Foundation Trust says there have been no more deaths at Scarborough Hospital of people who had the virus in the last week.
There have so far been 80 people who have died with coronavirus at Scarborough Hospital, and 134 at York.
The Trust has discharged 525 patients who had tested positive with coronavirus to continue their recovery.
Outside of the Trust, data from the Office for National Statistics released on Tuesday show there were no deaths outside of the Trust - either in care homes, hospices or people’s homes - from coronavirus in the week ending June 12.
Testing, which was originally only available for key workers, is now available to anyone of any age who is showing coronavirus symptoms.
Tests can be booked via the NHS website at https://www.nhs.uk/conditions/coronavirus-covid-19/testing-and-tracing/ask-for-a-test-to-check-if-you-have-coronavirus/
Tests for key workers can be booked at https://www.gov.uk/apply-coronavirus-test-essential-workers .
Across the UK, there have so far been more than 300,000 confirmed cases of coronavirus and more than 42,000 deaths.
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