The 2011 killing involved a former roommate and two others and occurred around the 10th anniversary of the Sept. 11, 2001, attacks, ABC News reported.
"We are looking at a possible connection with the suspect in the marathon atrocity and this active and open homicide in Waltham,'' Middlesex County District Attorney spokeswoman Stephanie Guyotte told ABC.
Tsarnaev, 26, was killed in a shootout with police early Friday. His brother, Dzhokhar, 19, was charged Monday in the bombing that killed three people and injured more than 170 others at the race's finish line.
The nearly decapitated victims of the 2011 killings were found in a Waltham, Mass., apartment, their bodies covered with marijuana.
Law enforcement officials also want to know if Tsarnaev had turned to radical Islam, The Wall Street Journal reported Monday.
He began studying Islam at the encouragement of his mother, Zubeidat Tsarnaeva, who felt he had slipped into a dissolute life of partying and womanizing. A champion boxer, he abandoned the sport because he came to consider it un-Islamic.
He began to push family members to adopt stricter lifestyles, his mother said, adding he convinced her to adopt more modest dress.
His father, Anzor Tsarnaev, was angered by the changes, the Journal said. He called his wife "crazy" for changing her way of dressing and was angered by his elder son's decision to drop his boxing career.
The parents separated about two years ago, and the father moved to Dagestan after falling ill. About the same time, Tamerlan Tsarnaev became more confrontational about his religion, arguing with worshipers at a mosque in Cambridge.
The challenges increased for him. He was charged with assault by a girlfriend who said he slapped her. His interest in college waned. A friend was the victim of a homicide.
Even with all this information, however, authorities say they still don't know what motivated Tamerlan Tsarnaev and his younger brother allegedly to set off two bombs at the Boston Marathon and shoot to death a Massachusetts Institute of Technology police officer.
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