It happened after American Eagle Flight 5811 landed around 4 p.m. Thursday at the Frederick Douglass Greater Rochester International Airport.
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Officials say the plane, an E-145 Embraer Regional Jet, had 50 passengers and three crew members on board.
Authorities say the plane landed safely on the main runway but then slid off the taxiway and veered into the grass.
American Airlines, American Eagles' parent company, said in a statement the plane slid due to snowy airfield conditions. The plane will be taken out of service for a full inspection.
"Safety is our top priority and we apologize to our customers for their experience," part of the statement reads.
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There were no injuries. Passengers were being moved to the terminal by bus.
The cause of this incident remains under investigation.