The mouse was invented by Douglas Engelbart in the year 1963. He belonged to the Stanford Research Institute which extensive research on usability testing. Engerlbert and his team had initially nicknamed the mouse 'a bug' and it was one of the pointing devices that were developed for his oN-Line System (NLS). Although there were other devices the mouse was though of as being extremely convenient since it was to be held under one hand, had wheels for movement as well as buttons that allowed the user perform simple functions. In the first mouse that was developed the rotation of the wheel was the equivalent of a move along the axis. The final patent for this device came on the 17th of November in the year 1970.
Hmmm...turns out to be Xerox in 1981 according to wikipedia
Xerox was the first - they also made the first GUI (Graphical User Interface) - One of the owners of Apple (I forgot which one) heard of what Xerox was doing and was invited to see it - Xerox had it and the GUI as an R&D project, and never copyrighted or patted the idea - Apple took it and ran with it - But it was Microsoft was took the idea from Apple and made the mouse and GUI a common ever day house hold thing via MS Windows 3.0. BUT the answer to the question is the R & D department at Xerox first made a mouse.