Bratton spoke Tuesday on "CBS This Morning.'' He said Ismaaiyl Brinsley seems to have had cash, in $100 bills, though he lived on friends' couches and doesn't appear to have been employed.
"Where did he get his money? Who does he hang out with?" Bratton said. "He's a couch crasher as they call him, he doesn't seem to have a residency, just crashes on somebody's couch."
It's not immediately clear whether Brinsley was carrying the cash when he killed himself after ambushing Officers Wenjian Liu and Rafael Ramos in their patrol car Saturday.
Bratton said investigators are checking into all of Brinsley's relationships.
Police also released surveillance video of Brinsley before the shooting and a picture of a jacket he was wearing the day of the shooting hoping someone will recognize him and come forward with information.
The surveillance video shows Brinsley at the Atlantic mall in Brooklyn holding a foam food container that investigators believe held the gun he used.
Police said Brinsley was a bystander during a protest in Union Square two days before a Staten Island grand jury decided not to indict an officer in the death of Eric Garner.
Prior to the shooting Saturday, police said Brinsely vowed in an Instagram post to put "wings on pigs'' and made references to Garner and Michael Brown.
"This has nothing to do with police retaliation," Brinsley's sister Jalaa'a Brinsley said. "He was an emotionally troubled kid. He needed help and didn't get it."
It remained unclear if Brinsley simply latched onto the cause at the end of a violent rampage that began Saturday morning in Baltimore when he shot his ex-girlfriend in the stomach. The woman said Brinsley had first held the gun to his head but she talked him down, authorities said.
Investigators believe Brinsley acted alone.
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