Gov. Dannel Malloy said this week that Connecticut would welcome Syrian refugees following the deadly Paris attacks.
Officials say one of the terror suspects posed as a Syrian refugee to get into Europe.
Now dozens of states say they won't accept Syrian refugees.
So far Connecticut has taken in 10 refugee families.
"We have an obligation as Americans to do our part in these situations, but do it at a very high standard with a good background system," Malloy says.