According to RCMP Cpl. Don Halina, the incident occurred during "an alcohol-fuelled fight" in the early morning hours of Sept. 27.
After checking into the nursing station to assess her injuries, Best was medevaced to Yellowknife the next day suffering from a possible fractured skull.
Halina said Best has since returned to Tulita.
He said both women sustained injuries in the altercation, although Best suffered the worst of it.
The unnamed woman has since been charged with assault causing bodily harm. She will appear in court in Tulita Nov. 20.
"The original incident wasn't necessarily reported as a beating," said Halina. "It was more of a fight."
He said no charges have been laid against Best.
"There's none anticipated at this time. We have no information to support a charge. The accused has refused to make a statement."
Best served as a Yellowknife city councillor from 1997 to 2000. Before that, she worked a number of years as the executive director of the Yellowknife Chamber of Commerce. After her council term ended, she made an unsuccessful bid for mayor.
She moved to Tulita to take a job as the executive director of the Tulita Yamouria Community Secretariat last March.
Best could not be reached for comment.