Assuming that the owner does not own any other rental properties, both the federal Fair Housing Act and Connecticut Fair Housing Act exempt landlords of owner-occupied multifamily buildings of up to 4 units. This means that the owner can legally decline to rent to a family with children.
However, it is still illegal to advertise a discriminatory preference or to "make statements" indicating such a preference. The owner can simply select a childless tenant without placing an ad that says "no kids". Federal exemptions are at 42 US Code 3603(b):
http://www.law.cornell.edu/uscode/text/42/3603