Federal investigators assigned to the fatal shooting of a 37-year-old Minneapolis woman are looking into her possible connections to activist groups protesting the Trump administration’s aggressive immigration enforcement, in addition to the actions of the federal agent who killed her, people familiar with the situation said.

It seems increasingly unlikely that the agent who fired three times at the unarmed woman, Renee Nicole Good, will face criminal charges, although that could change as investigators collect new evidence, the people added.

On Sunday, President Trump described Ms. Good and her wife, Becca Good, as being “professional agitators,” adding that the authorities would “find out who’s paying for it.” He offered no evidence to support his claims.

The decision by the F.B.I. and the Justice Department to scrutinize Ms. Good’s activities and her potential connections to local activists is in line with the White House’s strategy of deflecting blame for the shooting away from federal law enforcement and toward opponents they have described as domestic terrorists, often without providing evidence.