mid-14c., court, "short, concise, compressed," from Latin curtus "(cut) short, shortened, incomplete," from PIE root *sker- (1) "to cut." Sense of "rude, tartly abrupt" is attested by 1831.
The Latin word was adopted early into most Germanic languages (compare Icelandic korta, German kurz, etc.) and drove out the native words based on Proto-Germanic *skurt-, but English retains short (adj.), which also has a secondary sense of "rudely abrupt." Related: Curtal.