As of 2015, there is no official way to control an Apple iPad with a wireless mouse without illegally modifying the device. The only available interface devices include wireless keyboards, which connect via Bluetooth technology, and styluses that simulate finger input on the screen.
The Apple iPad uses an electrical engineering concept known as capacitive coupling, which lets you use your fingers to input commands on the screen. Capacitive sensing technology allows the device to sense the electrical current that passes through your fingers to detect their location. The iPad's operating system interprets the motion of your fingers and correlates them to commands that resemble clicking and dragging on a traditional mouse. As the iOS operating system functions through this system of motion input, it is not possible to use a wireless mouse as an input device.
In addition, the iPad's operating system and numerous apps contain controls that only respond to multiple input sources, such as touch from two or more fingers. As Apple wireless mice only have two buttons and a limited number of input sensors, it is difficult to recreate this feature. Even mice with multitouch sensors do not feature the same control area as the iPad.