In other larger districts with less staff, it may be less intense like a letter home. Some people own a home in a district, rent it out, and still use it as the home address. In less impacted areas, you can ask for an interdistrict transfer and receive it.
The spirit of the "rule" would preclude the child attending either district and would point to the child attending the school in the boundary area where he or she sleeps at night -- but lots of things like this do happen all the time and especially now with budget cuts it could be expected that districts may police it less. Alternatively with budget cuts districts may police it more and allow fewer "loose" attendance rules.
By calling each district you will get exactly what your options are.
Feel free to contact me with any questions.