The cocaine trafficking arrest of LaMar D. Cook , the deputy director of Governor Maura Healey’s Western Massachusetts office , has prompted the state’s Republican delegation to call for a thorough review of hiring and vetting practices in the executive branch, according to a letter sent to the Democratic governor.

The Republicans also want to know how Cook , 45, was hired. He was arrested Nov. 3, and immediately fired, has pleaded not guilty to trafficking 200 grams or more of cocaine, unlawful possession of a firearm, and driving without a license.

Meanwhile, Republican gubernatorial candidate Mike Kennealy Monday called for an investigation into hiring policies in the executive branch.

Investigators intercepted eight kilograms — or nearly 18 pounds — of cocaine addressed for de

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