Boston city councilors and the head of an advocacy group raised pointed questions Thursday about the vetting process Mayor Martin J. Walsh used to pick his new police commissioner, Dennis White, after a domestic abuse allegation surfaced against White just two days after his appointment.

“What kind of process was put in place to decide whether or not this man was ready to assume this position?” asked Councilor Julia Mejia during a phone interview.

Walsh announced Wednesday night that the city was placing White, a veteran member of the Boston Police Department, on leave and launching an investigation after a Globe reporter asked questions about the 1999 domestic violence allegation.

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