Let's examine the collection details page of "Connecticut, Births and Christenings, 1649-1906", which can be accessed by clicking the "Details" button in the search results. The list of entries to the left of the map contains our clue. Click the first entry which says "1649 - 1800 Connecticut, United States of America". The map will update to show the geographic area that is covered by Connecticut for that time period.
Connecticut owned the Northeastern corner of Ohio until 1800. It was called the Connecticut Western Reserve. Quoting Wikipedia:
The Connecticut Western Reserve was a portion of land claimed by the Colony of Connecticut and later by the state of Connecticut in what is now mostly part of northeastern region of the U.S. state of Ohio. The Reserve had been granted to the Colony by King Charles II. Following the American Revolutionary War, Connecticut gave up claim to some of its western lands, but sold the Western Reserve to developers initially. It finally ceded control of this portion to the United States, and the area was organized under the Northwest Territory, until Ohio was admitted as a state.