The person who opened fire at a megachurch in downtown Houston on Sunday was a 36-year-old woman who carried an AR-15 and had a yellow rope that “appeared to be a detonation cord” for a bomb, according to a search warrant for her home in Montgomery County.

The document provided new details of the shooting that rattled Lakewood Church, which is led by the televangelist Joel Osteen and is one of the largest congregations in the United States. The shooting ended quickly after the woman was shot and killed by off-duty police officers who had been hired to provide security.

The warrant identified the woman as Genesse Ivonne Moreno, who lived in Conroe, Texas, north of Houston. A boy who authorities have said is 4 or 5 years old and arrived with Ms. Moreno was wounded during the shooting. He was in critical condition on Monday. A man in the church was also wounded.

It remained unclear what connection the boy had to Ms. Moreno or what connection she had to Lakewood Church, where sermons by Mr. Osteen attract huge national audiences online and on television.

A motive for the shooting is also unclear. A reference to “Palestine” was handwritten on the rifle used in the attack, according to a law enforcement official familiar with the investigation.

Before she was shot and killed by the off-duty officers, the shooter stated that she had a bomb, according to the warrant. The officers said she was carrying a yellow cord that “appeared to be a detonation cord” that was “consistent with the manufacture of explosive devices.” The officers opened fire after she pointed her weapon at them, according to the warrant.