Five attacks took place within hours of each other on Friday, killing three and critically wounding two others, within a three-mile (5km) radius.
All the victims were black and police say there are searching for a white male in connection to the attacks.
Community leaders have tried to calm fears of further attacks.
The police said they were searching for a white man driving a white pick-up truck, who was seen in the area of three of the shootings.
The BBC's Jonathan Blake says the crimes have shocked people living in a relatively quiet part of north Tulsa, and that there is a fear that the killer may strike again.
Our correspondent says detectives are hoping for people to help them, but that many in the community do not trust the police.
'Nervous' Tulsa police chief Chuck Jordan said they were investigating whether the attacks were hate crimes, after investigators earlier said the incidents were linked.
The FBI has joined a task force set up to investigate the killings, he said.
Jack Henderson, a city councillor for the district where the attacks occurred, urged people to come forward with information.
"This is Tulsa, Oklahoma. We should have the ability to stand out on your porch anytime, day or night, that you want to, to walk down the street, day or night.
"And the only way that this person is going to be brought to justice is we need some leads."
A 49-year-old was the first killed at about 01:00 local time (06:00 GMT) on Friday.
Minutes later the gunman approached two other men and asked for directions before shooting them. They survived but later two more were shot dead nearby.
"We're all nervous," said one resident, 52-year-old Renaldo Works. "I've got a 15-year-old, and I'm not going to let him out late. People are scared. We need facts."
"You don't want to be a prisoner in your own home," he said.
Manhunts in Olkahoma
Originally Posted by Sphere
