The statement says Anthony Heffernan was battling a drug addiction and fought constantly to keep clean.
Natalie Iaquinta says her brother had a relapse on March 15, the day before he was killed.
She says police investigators told her family that hotel staff called police when Heffernan failed to check out at 11 a.m.
Iaquinta says her brother had a lighter and syringe in his hands when police busted into his room after trying for about 30 minutes to get him to open the door.
She says police Tasered Heffernan twice, then one officer shot at him five times.
"He was struck three times in the head and once in the chest and [another bullet went through the window]," Iaquinta said.
Neither police nor the province's police watchdog have confirmed the details.
"(How does) a young man who was in medical distress, who was causing no public disturbance other than missing checkout time, warrant five police officers... busting down his door, thereby escalating the situation?" the family asked in its statement.
Relatives are also questioning why it took police 11 hours to notify them of his death.
"Why (couldn't) a man who had no weapons ... be detained in another way, and is it protocol to fatally shoot someone if a Taser is unsuccessful?"
The family said Heffernan hated relapsing and worked to prevent it.
"He phoned his parents and sister every day, sometimes twice, to help him with staying clean. If he weakened in his battle, he would find a hotel room away from friends and family. Here he could remove himself and keep his issue at a distance from others."
Investigators have said Heffernan was agitated and in medical distress when they went into the room.
The funeral service for Heffernan was to be held Wednesday in Prince Albert, Sask. His obituary says Heffernan loved baking and his specialty was chewy double-chocolate-chip cookies.
It says he loved riding snowmobiles, motorbikes and hunting when he was at home. He also enjoyed taking care of litters of German shepherd puppies.
Heffernan graduated from St. Mary High School in Prince Albert in 2006. In the fall, he took the electrician apprenticeship program in Alberta, and was set to write the final exam for the masters electrician program.
There have been two other police-involved shootings in Alberta in the last few days. On the weekend, a Calgary officer shot and critically injured a 30-year-old man in an alley shortly after the man taunted demonstrators at an anti-racism rally. Police say he confronted the officer with a metal pipe.
On Monday, a 40-year-old man was taken to hospital with potentially life-threatening injuries after he was shot by at least one RCMP officer in the community of Wetaskiwin south of Edmonton. Police say Mounties were responding to a call at an apartment complex.
ALSO ON HUFFPOST: