Two Covid cases had already been reported from the building, Oi Fai House in Yau Oi Estate.
The preliminary positive cases involve a 66-year-old man and a six-year-old. Both developed a runny nose at the beginning of April.
They live in units that face in the same direction as one of the earlier cases.
Dr Chuang Shuk-kwan from the Centre for Health Protection said experts are investigating how the virus was transmitted there.
“We suspect there may be some environmental contamination or environmental transmission. Site visit has been arranged for the experts and other government departments to inspect the place,” she said.
This comes as the Centre for Health Protection reported 14 new coronavirus infections, two of which are locally acquired.
Officials are unable to trace the source of the infection of a 42-year-old woman, who is a salesperson at a Mannings shop in Yuen Long.
She developed a headache on March 26 but didn’t take a Covid test until almost two weeks later.
Dozens of her colleagues and relatives will be put under quarantine.
The 12 imported cases involve people who flew in from the Philippines, Indonesia, India, Egypt and Canada.