The logo was "an extension" of designs and drawings Leonard had made since he was in college.
Leonard was a Nike athlete until September 20, 2018, when the deal expired.
The lawsuit, obtained by KSAT-12, claims Leonard designed and authored the logo before he signed with Nike.
Leonard was a Jordan Brand athlete for his entire National Basketball Association career until the two sides ended negotiations a year ago.
Kawhi Leonard is filing a lawsuit against Nike.
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"Several years later, as part of an endorsement dealt with Nike, Leonard allowed Nike to use on certain merchandise the logo he created while Leonard continued to use the logo on non-Nike goods", the lawsuit says.
In the lawsuit, Leonard said Nike filed a copyright application for a logo that he designed and did so "unbeknownst to Leonard and without his consent". In March, the company told Kawhi that "it owns all intellectual property rights in the Leonard Logo and demanding that Leonard immediately cease and desist from what Nike claimed was the unauthorized use of the Leonard Logo".
Leonard claims that he developed the logo himself by tracing his very large hands. The ring and pinky fingers of the logo are shaped into a "K", the middle finger and thumb form an "L" and the index finger is created to resemble an elongated "2" - all nods to his initials and jersey number.
His Raptors are even with Golden State in the championship series at 1-1 heading into Game 3 on Wednesday.
Leonard will become a free agent in July and is widely believed to be considering signing with the Clippers regardless of the outcome of the Finals.