Electrons, muons, tau, and the neutrinos all talk to the electro-weak force but not the strong force.
Quarks talk to both the electro-weak and the strong force
Both classes of particles talk to gravity.
From several different studies (e.g. the rotation of galaxies) we get some strong indication that something's missing in the picture. Either gravity is very much stranger than we think (MOND theories) or there's some kind of matter flying about that doesn't talk to either the electro-weak or strong forces.
If the Big Bang is correct, all matter and energy came from the same elementary particles--both the matter we know and the dark matter. So, if there is dark matter, somehow it has to connect to ordinary matter. But how?
Via gravity? I haven't tried to run numbers on that, but I don't see how you generate a preponderance of dark matter particles that way. I could be wrong--I haven't run the numbers.
Otherwise you need a new force. If electrons or quarks talked to the new force, we'd have seen effects--the dark matter wouldn't be dark.
But if neutrinos talked to the new force, it would be very hard to tell, since it is already hard to see neutrinos.
A new force would probably use at least one boson--like the photons we know and love--and the dark matter be at least 1 and I suspect more likely 2 fermions. The dark matter particles and the new force is called the "dark sector." If this "dark sector' exists, and if neutrinos can feel the "dark force," the effects would be subtle. We can't a priori say what those effects would be--too many unknowns (such as--how many different kinds of dark particles are there?). But we could look for anomalies.
I've done some naive calculations. A galaxy seems to have a distribution of dark matter that decreases with radius. Since the stars at its center are generating neutrinos all the time, scattering of neutrinos off dark matter should tend to push the dark matter farther away. The calculation's upshot was that the coupling of neutrinos to dark matter had to be less than some ridiculously large value, so I wasn't going to learn anything by trying a more precise study. Similarly with SN1987A#Neutrino_emissions, or that IceCube actually observes high energy neutrinos instead of having them scattered away.
The neutrino anomalies will probably be more fruitful.