It aims to help stem the spread of coronavirus by identifying people who are infectious, but don't have the usual physical symptoms associated with the virus.
Symptoms of the virus include a high temperature, a continuous cough and a loss or change to your sense of smell or taste.
However, around one in three people with Covid-19s have no symptoms and will spread it without realising.
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Councillor Salma Arif, Leeds City Council’s executive member for public health, said: “We’ve launched this initiative to help drive down transmission rates.
"Increased community testing is a vital additional tool at our disposal to help identify those who are infected and infectious, but unaware that they might be spreading the disease.
"Broadening testing to identify those showing no symptoms will mean finding positive cases more quickly, and breaking chains of transmission.
“I’d encourage as many asymptomatic residents as possible to take advantage of this new service. By doing so, they’ll not only be protecting themselves, but also all those around them.”
The council is offering a number of options across the city for residents to take part in community testing including ordering a test to your home, getting a home test from a pharmacy or collecting a test at a local test site.
People can also go to a community testing site.
The sites are for people with no symptoms and anyone with Covid-19 symptoms should self-isolate and book a test.
These sites are at Leeds Beckett University, Armley Community Hub & Library, City Centre Community Hub, Deacon House Centre, Dewsbury Road Community Hub & Library, Halton Library, The Compton Centre Community Hub & Library and The Reginald Centre.
Residents should have two tests during a week-long period.
Full list of sites testing people with no symptoms:
Armley Community Hub & Library, 2 Stocks Hill, Armley, LS12 1UQ
City Centre Community Hub, Woodhouse Lane, LS2 8LX
Deacon House Centre, Seacroft Avenue, Leeds, LS14 6JD
Dewsbury Road Community Hub & Library, 190 Dewsbury Road, LS11 6PF
Halton Library, 273 Selby Road, LS15 7JR
The Compton Centre Community Hub & Library, Harehills Lane, Harehills, LS9 7BG
The Reginald Centre, Chapeltown Road, Leeds, LS7 3EX.
Opening hours 10am to 4pm Mon to Fri and 10am to 1pm Saturday except City Centre Community Hub which doesn’t open Saturdays.
Leeds Beckett University - City Campus LS1 3HE (Monday to Friday 8.30am to 2pm) Headingley Campus LS6 3QS (Monday to Friday 9am to 2pm).