More than a dozen shots were fired in Lawrence early Sunday morning in front of a house where a birthday party earlier for a 7-year-old child had turned into a party for adults.

Police today are trying to determine if two men hospitalized with gunshot wounds after the incident are innocent victims or combatants.

“We’ve got more questions than answers,’’ Lawrence Police Chief John Romero said in a telephone interview today.

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According to Romero, when his officers were on the scene assisting one of the victims of gunfire on Brook Street, officers heard more shots being fired. Officers raced around the corner and recovered a firearm and arrested one man for illegal possession of a firearm.

One man was transported from the scene to a Boston hospital with bullet wounds that were not considered life-threatening, and Romero said city detectives hope to interview him this week once his medical condition improves.

The chief said his officers also want to question another man who showed up at Lawrence General Hospital many hours after the gunfire. The man had multiple gunshot wounds to his lower extremities, and is expected to recover, Romero said.

“If you are totally innocent, and if you are shot, why would you not just go to the hospital immediately?” Romero said.

Romero said that more than a dozen spent shell casings were recovered at the scene.

“We found numerous shell casings, which leads us to believe at least two guns were involved, perhaps even more given the number of shell casings,’’ Romero said. He declined to be more specific about the ballistic evidence, citing the ongoing investigation.

Romero said the gunfire broke out in front of a house on Brook Street, where the resident told police she held a birthday party for her 7-year-old child that eventually grew into a party for adults. The gunfire was reported around 3 a.m.

Romero said it was not clear what the connection was between the gunfire and the party. He also said police did not know what sparked the gunfire.

“We don’t have a motive,’’ Romero said.