Dahlia Group, the carrier whose bus flipped over in Madison on Monday, injuring 36, has been cited with 35 violations since January 2014, according to the Federal Motor Carrier Safety Administration.

The violations range from having inoperative windshield wipers and driving more than 15 mph over the speed limit to having an on-duty driver in possession of an alcoholic beverage.

Dahlia has two branches, and the bus involved in Monday's accident was registered to a Boston-based branch that was cited for four of the 35 violations.

The other 31 violations were cited to a branch based in Flushing, N.Y.

According to Mohegan Sun spokesman Cody Chapman, the bus was heading to Mohegan Sun from New York.

By the safety administration's standards, the New York-based Dahlia's violations mean almost 65 percent of motor carriers in the same category have better on-road performance than it does.

Records show Dahlia's New York hub has five vehicles and six drivers and has been inspected 47 times.

At the Boston hub, where there are 12 vehicles and 15 drivers, the six inspections that have occurred since August of 2014 have found four violations.

The safety administration website lists the violations for both branches as having occurred in multiple states, including New York, Pennsylvania and Connecticut.

Massachusetts corporations records show that Dahlia Group was established there in November 2013. The New York-based company first filed papers in May 2004, records show.

The 12:24 p.m. accident, which occurred just east of Exit 61 on Interstate 95 north, shut the northbound lanes down for four-and-a-half hours as emergency responders from several towns worked to rescue passengers.

The driver of the bus, Keyi Zhang, 63, of Flushing, N.Y., told state police he was merging from the left lane to the right and lost control on the snow-covered road.

He then struck the guardrail on the right side of the road.

Zhang was taken to Shoreline Medical Center in Westbrook for treatment of a possible injury.

Officials with the New York Department of Motor Vehicles said by email Tuesday that Zhang has a valid Class B New York commercial driver's license with passenger endorsement and that he's medically certified to drive.

Officials said Zhang has no suspensions, revocations or accidents on his driving record.

Police said 36 of the bus's 55 passengers were taken to nearby hospitals and clinics with minor to moderate injuries.

Speaking at a news conference Tuesday morning, Yale-New Haven Hospital officials said they initially received 16 patients, four of whom were critically injured.

Six more patients, half of whom were listed in critical condition, came in from Middlesex Hospital later in the day, officials said.

Dr. Kimberly Davis, chief of general surgery, trauma and surgical critical care, said a "fair number" of the patients evaluated Monday remain at the hospital.

She said those who remain in critical condition aren't in "grave danger."

Injuries included broken bones and lung punctures. Some patients had bled enough to require blood transfusions, she said. Others needed procedures in order to be stabilized.

Davis said she couldn't go into any more detail than that.

She said hospital employees had been relying heavily on interpreter services while treating the injured because a number of the injured speak little to no English.

Davis expected that some patients would be released Tuesday, but said others will remain hospitalized for longer periods of time.

l.boyle@theday.com

Twitter: @LindsayABoyle