The investigation has been set up by the Independent Office for Police Conduct (IOPC).
Today (Thursday, August 4), Sussex Police said it is supporting the independent inquiry.
Sussex Police added that it made a voluntary conduct referral to the IOPC, which is the usual practice and were notified by the IOPC that it would be carrying out an independent-led investigation.
Police officers were called to the care home in St Leonards on the afternoon of Tuesday, June 21 following a report that a 93-year-old resident with dementia had a knife and was threatening staff.
Sussex Police said on arrival, police officers were shown by care home staff into a room where the man was residing.
Officers briefly engaged with the man, with one of the officers using incapacitant spray, followed by a baton.
Sussex Police said the second officer deployed a Taser before the knife was removed from the man and he was handcuffed.
Police added that the man was taken to hospital following the incident for medical treatment.
He remained in hospital where, sadly, he died three weeks later on Wednesday, July 13, police said.
Sussex Police have confirmed that the man was Donald Burgess, aged 93.
A post mortem has been carried out and the findings of further cardio-pathology examinations are awaited, as the cause of death is not yet known, police said.
Sussex Police added that gross misconduct notices have now been served by the IOPC on the two officers involved, both police constables, along with letters advising them they are under criminal investigation for manslaughter. These actions do not necessarily mean disciplinary proceedings or criminal charges will follow.
Assistant Chief Constable Tanya Jones said: “We want to express our sympathies to the family and friends of Mr Burgess.
"Our thoughts remain with them at this difficult time.
"We are providing every assistance to the IOPC to allow for a thorough investigation and for the family to receive the answers they need.”