Mr. Bowers did not fall into any category barred from gun ownership under federal law, including felons, convicted domestic abusers, dishonorably discharged veterans, or people adjudicated to be mentally ill or subject to certain restraining orders.

He also had a handgun license, an A.T.F. spokeswoman, Charlene Hennessy, said.

Ms. Hennessy said the A.T.F.’s investigation found that Mr. Bowers owned 10 guns in total, all purchased and possessed legally: the four found at the synagogue; three handguns and two rifles recovered from his residence; and a shotgun recovered from his car outside the synagogue.