Kent Police has confirmed the fire at Invicta House tower block in Margate on Sunday (April 1) is being investigated as suspected arson.
Firefighters were called to the Millmead Road tower block at 8.36pm, their third call to the site in a week.
Seven fire engines and the height vehicle attended the scene. The blaze was found on the stairwell between the second and third floors.
Some families were unable to leave the building because the fire blocked their exit.
Councillor Gary Taylor, who was at the scene, said that four people were taken to hospital due to smoke inhalation.
Residents say that East Kent Housing staff, who manage the block, carried out a clean up of the site and said security would be reviewed.
Fire crews were also called to two rubbish chutes fires at Invicta House on March 25 and March 28. Police had been investigating an incident that took place on March 28 but later said it was no longer being deemed as suspicious.
A Kent Police spokesman said: “Kent Police was made aware of a fire at a property in Millmead Road, Margate, at 8.38pm on Sunday 1 April.
“The fire is being treated as suspicious and enquiries are ongoing.
“Anyone with information is urged to call 01843 222289 or Kent Crimestoppers anonymously on 0800 555 111 quoting 01-1102.”