SALEM, Mass. — Blood and lighter fluid stained her clothes and slash wounds marked her neck when Tanicia Goodwin walked to a police station, smashed a display case in the lobby and collapsed to the floor.

Minutes earlier, Goodwin had slashed both her children’s throats, soaked them with lighter fluid and set their apartment on fire, according to prosecutors and emergency officials.

But Goodwin didn’t initially tell police much Sunday night. “I did what I had to do to protect my children, I’m sorry,” Goodwin kept repeating to a police interviewer, according to authorities.

Her 8-year-old son, Jamal, was more specific as he was being treated, though he couldn’t talk and was struggling to breathe.

“The paramedic asked if his mother did this to him and he nodded yes,” prosecutor Melissa Woodard said at Salem District Court on Monday.

Jamal was in critical condition and Goodwin’s 3-year-old daughter, Erica, was in stable condition Monday after both underwent surgery at Children’s Hospital in Boston, officials said.

Goodwin was ordered held without bail and scheduled to appear in court next week. A judge will then decide if she’s eligible for bail on charges including two counts of assault with intent to murder and arson.

Goodwin, 25, didn’t enter a plea and spoke only to indicate that she wanted the court to appoint her an attorney. That attorney, Steven Van Dyke didn’t immediately return a call for comment. No possible motive was disclosed by either the prosecutor or Goodwin’s lawyer.

Later Monday, several residents outside the building where Goodwin lived at the high-rise Salem Heights Apartments declined to comment. The door to Goodwin’s building was locked to non-residents. The building is owned by a nonprofit group, Preservation of Affordable Housing.

Prosecutors said Goodwin didn’t just set the fire and leave her son inside, but she also disabled the apartment’s smoke alarms, removed the interior doorknob and blocked the vents and nearly every sprinkler with duct tape. She also left her daughter alone in a neighboring apartment, face down and bleeding on a couch, Salem Fire Chief David Cody said.

“Almost everyone has asked that same question: ‘What went through her mind?’ ” Cody said.

Firefighters responded to the blaze Sunday night and saw the girl with her mother and two other adults in a neighbor’s apartment. But they didn’t notice the girl was wounded as they headed to the fire in Goodwin’s apartment, Cody said.

He said the fire started on a couch, and Lt. Richard Arno used a hallway extinguisher to knock it down enough to get a look around. Soon after, he found Jamal sitting against a wall with a neck wound so severe his trachea was exposed. Arno carried the boy out, and firefighters extinguished what turned out to be a minor blaze.

Firefighters making sure the area was cleared out before leaving found Erica alone in the neighbor’s apartment with her throat slashed, Cody said.

“It was basically just going back and checking everything and they just happened on the girl,” he said.

Prosecutors said nurses had to wipe lighter fluid off both children before they could be treated.