Gov. Maura Healey said an investigation into the death of a Massachusetts State Police recruit this month by an outside attorney should play out first before federal investigators get involved.

Enrique Delgado-Garcia died earlier this month after suffering injuries sustained while working out in a boxing ring at a state police academy in New Braintree. His family told NBC10 Boston and Telemundo Nueva Inglaterra that his neck was broken, his body was covered in bruises, and he had missing teeth.

Attorney General Andrea Campbell appointed David Meier, a partner at Todd & Weld, to look into Delgado-Garcia’s death after Worcester County District Attorney Joseph Early said his office would not handle the investigation because of close ties to the recruit.

At an unrelated event Tuesday afternoon, Healey did not say if she supported calls for a federal investigation into the state police academy but said Meier’s probe needs to move forward.

“Let’s let the attorney general and the appointment of her special assistant attorney general — let’s let that investigation go forward,” she said.

Healey said she was “grateful” for Meier’s appointment.

“He appears to be a highly experienced and respected prosecutor, and I’m sure he’ll assemble the team and do the work. From the beginning, I have called for an investigation of this tragic death, and it’s something that we owe to Mr. Delgado-Garcia’s family. The public also deserves answers as well,” she said.

In a statement Monday, Healey said she plans to direct incoming State Police Col. Geoff Noble to review academy training and policy practices “to ensure they serve the men and women of the state police.”

The governor also said she suspended boxing training at the state police academy.

“I hope that that investigation proceeds promptly,” she said at the State House Tuesday.