The corvette sank with the loss of 46 lives on the night of March 26, 2010 near the South's disputed Yellow Sea border with the North.
An investigation by a South Korean-led international commission concluded it had been sunk by a torpedo from a North Korean submarine -- a charge Pyongyang has always angrily denied.
The documentary highlights theories that cast doubt on the commission's findings. It cites experts who question the findings of the probe, including one who suggested the warship probably sank after colliding with a submarine of unknown origin.
But the court at Uijeongbu near Seoul rejected the injunction, saying the movie had not distorted facts or tarnished the reputation of the victims as claimed by the complainants.
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"The movie merely displayed opinions that differed from the result of the international commission, which does not amount to defamation," it said in a ruling.
"Production and screening of movies are guaranteed by the freedom of expression enshrined in the constitution."
The movie is scheduled to hit theatres across the country tomorrow. It is unclear whether the complainants will appeal the court's decision.
Cross-border tension surged after the Cheonan incident, with Seoul suspending most trade and aid with North Korea.
In November the same year the North shelled a South Korean border island, killing four people including two civilians and sparking brief fears of a full-scale conflict.