The inferior hand should just tag along, using the same muscle groups in the same sequence as the dominant hand - thus writing mirror script. And while the letters might look a wee skewed, as the muscular modulation is less trained, this normally should yield legible handwriting.
Reason: The mechanical part of the task of writing is triggered from the
premotor cortex and "saved" there as a series of movements, which always are repeated in the same sequence. This is called "procedural memory". So in a timed cascade, it activates the motoneurons in the motor cortex that control the muscles in your hand and forearm to make these move.
(Almost) Every neuron in the
motor cortex sends the impulse down to the corresponding motric neurons in the spinal cord. And it also sends some impulse to contralateral neurons, both on the cerebral as on the spinal levels. So when you relax the contralateral inhibition, it triggers the same move on the other side, too - which normally is suppressed.
And as the muscles are arranged in a mirrored fashion, the result of those movements also is mirrored. Presto, bingo! Mirror script.