He asked the Congressional Research Service to investigate, and it reported that all four Connecticut congressmen backed the amendment in a January 1865 vote.
A spokesman for Dreamworks Pictures, which produced Lincoln, did not immediately respond to an email seeking comment.
Courtney praised the film's acting and cinematography but said artistic license does not permit it to inaccurately put Connecticut on the wrong side of history, particularly on an issue as powerful as slavery.
In a letter to Spielberg, the four-term Democratic congressman includes a tally of the 1865 vote by the state's congressional delegation and a passionate defence of the state's role in emancipating millions of blacks.
"How could congressmen from Connecticut - a state that supported President Lincoln and lost thousands of her sons fighting against slavery on the Union side of the Civil War - have been on the wrong side of history?" he said in his letter.
Courtney, who majored in history at Tufts University, asked that the movie, which stars Daniel Day-Lewis as Lincoln, be corrected before its release on DVD.
Lincoln, which leads the Oscars with 12 nominations, also stars Sally Field as Mary Todd Lincoln and Tommy Lee Jones as Thaddeus Stevens.
- AAP