SEATTLE -- Seattle was paralyzed at midday Wednesday by two shootings that occurred within half an hour of each other in two of the city’s most congested areas, sparking massive manhunts for what initially appeared to be two different suspects.

The first shooting occurred about 11 a.m. at a popular cafe near the University of Washington. An unidentified gunman opened fire on five people, killing two of them and critically wounding the others.

Half an hour later, a woman was shot and killed in an apparent carjacking in downtown Seattle in a parking lot near the city’s Town Hall lecture center. Witnesses said the suspect fled in a black sport utility vehicle. A short while later, a vehicle matching the description was found abandoned in another part of town.

At least five schools and two community centers were placed on modified lockdown near the university district as police fanned out in a dragnet, cordoning off several blocks and conducting intensive, building-to-building searches. Witnesses described watching police, with guns drawn, question one man matching the description of the shooter in the cafe. The man was then let go.

The shootings came a day after Seattle Police Department leaders were called before the City Council to address the wave of gun violence that has plagued the normally tranquil city. There have been 19 homicides in the city this year, compared with 21 during all of 2011.

[UPDATED: 2:20 p.m., May 30:] Later, police said it was not yet clear that the two shootings were unrelated. They also raised questions about whether the downtown shooting was actually a carjacking or whether the victim may have known the gunman.

“We don’t know what their relationship was, if any,” Assistant  Police Chief Mike Sanford told reporters. “We don’t know the connection between the man and the woman here, but we’re working on it.”

In a statement, police said they were investigating a possible connection between the two shootings.

“There has been speculation that this shooting [downtown] may have been linked to the earlier shooting on Roosevelt Way NE [in the university district]," department spokesman Mark Jamieson said in the statement. “At this point, we just don’t know. Detectives are exploring every possibilty.”

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kim.murphy@latimes.com