Sinn Fein Foyle MLA Martina Anderson
A police officer was also injured during the incident.
The shooting is now being investigated by the Police Ombudsman.
Said the Foyle MLA: “I am shocked that a vulnerable man has been shot and wounded by police following a call-out to a home in the Waterside after midnight.
“The man is in intensive care in hospital and my first thoughts are that I hope he will survive his injuries.
“A police officer also suffered a stab wound during the incident.
“Thankfully the officer has been released from hospital and I hope he too makes a full recovery.
“I am deeply shocked that a vulnerable man has been shot by police.
“I have contacted senior police and the Police Ombudsman to convey my grave concerns that lethal force has been used in this incident.
“The PSNI needs to be provide the public with a full explanation about this shooting of a vulnerable man.”
