"The MLA jumped from the fourth floor of Room 411 and fell on a tin shed. He is dead," police said.
A suicide note found on the 70-year-old MLA's body said he was taking the extreme step due to acute depression and a number of other ailments including kidney-related problems for some time, according to the police.
Chief Minister Mamata Banerjee and Industry and Commerce Minister Partha Chatterjee visited the hostel and the hospital where the body was kept. Banerjee said that she could have helped Quasem in his treatment had she been informed, but he died before she could be introduced to him in the new Assembly.
She instructed authorities to hand over the body to the family after postmortem and other formalities on May 30.
The chief minister expressed her condolences to the bereaved family and asked the administration to accord him due honour and respect.
"If we receive any suggestion from the CPI(M), we will do the needful," Banerjee said.
Quasem was first elected to the West Bengal Assembly in 1977 from Baduria and Swarupnagar in the period between 1991-2006. He was recently elected from Basirhat North.
The CPI-M leader, who was a MP of the Upper House from 1984 to 1990, was the Rajya Sabha Vice-Chairman from 1987 to 1988.
Quasem is survived by his wife, a son and a daughter.
Chatterjee said that there should be an inquiry on what led the CPI-M leader to his tragic end.
Quasem was among the MLAs who had arrived here for the election of the West Bengal Assembly Speaker on May 30. With Quasem's death, the number of CPI-M MLAs in the Assembly has gone down to 39 and that of the opposition Left Front to 61.