That company, Eversource, said 50 to 69% of customers could lose power and restorations could take from eight to 21 days. Eversource serves 1.25 million customers.
Meanwhile National Grid reported over 28,000 customers were affected by outages in Connecticut.
Connecticut also banned empty tractor-trailers, tandem tractor-trailers, and motorcycles on Interstate 95 for most of the day until 5 p.m.
Henri weakened to a tropical depression Sunday night, but could still bring heavy rainfall and flooding across the Northeast and New England.
TRAVEL BAN LIFTED
Connecticut Gov. Ned Lamont announced he will be lifting a travel ban at 5 p.m. that went into effect on Sunday morning on all empty tractor trailers, tandem tractor trailers, and motorcycles on Interstate 95.
The Democrat urged people to stay off the road until the storm completely passes the state.
Storm-related flooding was blamed for major delays in the Hartford suburb of Wethersfield along Interstate 91, a major artery through Connecticut's capital city.
Brian Foley, special assistant to the Department of Emergency Services and Public Protection, said there was "water over the roadway on multiple lanes" and a couple accidents.
The northbound lane was closed for a short period and traffic was rerouted.
Eversource, Connecticut's largest electricity supplier, reported 32,902 of its 1.28 million customers in the state were without power as of mid-afternoon.
Communities in rural portions of eastern Connecticut had the largest proportion of power outages in the state by mid-afternoon on Sunday.
The small town of Canterbury had the largest percentage of customers without electricity, nearly 95%, according to Eversource. About 2,180 of the 2,305 were without power. Downed trees were to blame for many of the outages. In nearby Lisbon, 1,205 of the company's 1,891 customers were without electricity.
"We've had trees come down on swimming pools and on several houses. But fortunately, none of those incidents resulted in anybody being hurt," First Selectman Thomas Sparkman said.
Storm-related flooding from Henri has caused major delays in the Hartford suburb of Wethersfield along Interstate 91 northbound, a major artery through Connecticut's capital city.
Brian Foley, special assistant to the Department of Emergency Services and Public Protection, tweeted that traffic was reduced to one lane and there were multiple accidents.
Traffic cameras showed numerous vehicles backed up. Connecticut Gov. Ned Lamont on Twitter urged motorists to "avoid the area while crews work to address the situation."
"Stay safe, stay home" and prepare, with three to five days of food stocked, Gov. Ned Lamont advised Saturday.
He told residents that the heavy rain from the direct hit from Henri could pose a significant threat, with the ground already saturated from recent storms.
Lamont's emergency declaration enabled the state to take any actions necessary that may arise because of the storm.
Governor Lamont also urged coastal residents to know their shoreline evacuation zone in case of a flooding emergency.
All Stamford residents were advised to take the following precautions:
-Sign up for Emergency Alerts at www.ctalert.gov
-Stay in touch with the City of Stamford through our web site www.stamfordct.gov and the City's Emergency Hotline 203-977-8840
-Follow the City of Stamford's social media channels for updates including Facebook, Twitter, Instagram, or NextDoor.
-bring inside any lawn furniture, outdoor decorations, hanging plants, trash cans
-Charge cellphones/ withdraw cash in the event of power outages.
-Prepare an emergency kit
A full list of precautions and suggested preparation steps can be found at www.bepreparedStamford.org and www.ready.gov/hurricanes .
(The Associated Press contributed to this report.)
Additional Henri Coverage
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Connecticut braces for Henri
Emergency Resources for severe weather
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Weather or Not with Lee Goldberg's extreme weather survival guide
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