GodMark2
Master Poster
What happens when it comes into contact with matter?
Let's answer this by looking at what happens when normal matter 'comes into contact'. We'll use your hand, and the table it's resting on.
As your hand moves toward the table, several forces are acting on it. Mostly the force applied by your muscles. EM and Gravity are there, but so small that their effects can be ignored. Gravity because there's not enough mass to make much of it. EM because the difference in any attraction to protons and any repulsion to electrons in the table is very small.
As you get closer, however, things begin to change. Gravity is still minuscule, but the EM forces between the electrons in your hand begin to repel the electrons of the table. When the electrons in your hand are as far from the electrons in the table as the tables electrons are from their protons, you have four times as much force repelling the mutual electrons as you have attracting the protons to the electrons. Eventually, this force exceeds your muscles' ability to push the hand closer.
It's that transition from "very far away the net force is zero" to "close up the net force is huge" that we call 'contact with the table'. It all depends in electromagnetism. If dark matter doesn't interact with EM in any way, then it can never come 'in contact', with either itself, or 'ordinary' matter.
Summary: Dark Matter can never "come in contact" with anything, so asking "what happens when it does" doesn't make much sense.