Six nursing homes have been cited by the state Department of Public Health (DPH) for lapses in care, including two cases in which residents died. DPH fined Hancock Hall in Danbury $10,000 in August in connection with three incidents, including the case of a resident who died in June from complications due to a head injury caused by a fall out of a lift, the state citation said. Four days before the death, the resident was kicking and punching two nurse’s aides who were moving the person in the lift, the citation said. A clip on the lift pad came undone and the resident slipped out of the sling and onto the floor and sustained a head injury. A review found that the aides should have stopped the lift and notified a nurse when the person became combative.