Open enrollment for health insurance coverage began Wednesday and runs until Dec. 22.

At Ferguson Library in Stamford, officials held an enrollment session.

Some people there said they had concerns about signing up, so Access Health, the state's health care marketplace, sent representatives to answer some of their questions.

One potential customer said she was told premiums could go up an average of about 30 percent.

A spokesperson for Lt. Gov. Nancy Wyman, who is the board chair for Access Health, says that's not exactly true -- about 75 percent of the residents who saw their cost sharing reduction subsidies decline now qualify for advanced premium tax credits instead.

People who didn't have the CSR benefit could see their costs increase, but Access Health says it will reach out to those people to explore more affordable options.

Others said they were concerned by President Donald Trump's efforts to overhaul the Affordable Care Act.

One man who signed up for health care through the exchange said he was just thankful to have coverage.

"I thought the premiums were pretty good, compared to what I was paying United Healthcare a month," said Elon Mileikowsky, of Stamford. "We were paying a fortune in insurance. Oh God, I get sick when I think about it."

Access Health says it will have continue to have enrollment fairs throughout the state until mid-December.