Eversource Energy will have power restored to most of the state by 8 p.m. Saturday, a spokesman said.
Tens of thounsands of residents lost power following a gusty Christmas storm that brought more than 2 inches of rain to most of the state.
As of Saturday morning, about 3,400 customers were still without power, most of them in the western part of Connecticut.
“We continue to make solid progress,’' said spokesman Mitch Gross. “We have hundreds of line and tree crews at work.”
The utility company came under intense criticism earlier this year for what critics called a slow response following Tropical Storm Isaias, which took down trees and knocked out power for as long as nine days in some parts of Connecticut in August.
In advance of the Christmas Day storm, Eversource brought in extra crews from out of state and cancelled the vacations of its own employees to handle the additional work.
“The forecasters told us to expect very high winds and very heavy rain and that’s what nature delivered,’' Gross said.