All particles are either fermions, with total angular momentum J=0.5+N, or bosons, with total angular momentum J=0+N, in each case for N=0, 1, 2, 3 . . . and the lower possible boson values for total angular momentum (aka "spin") have names.
spin-0 is called "scalar"
spin-1 is called "vector" and
spin-2 is called "tensor"
A recent measurement made by the ATLAS experiment at the Large Hadron Collider (LHC) set upper bounds on the cross-section of interaction between hypothetical scalar and tensor (i.e. spin-0 and spin-2) dark matter particles and the particles of the Standard Model.
These cross-sections of interaction can't be more than something on the order of 10-42 for scalar dark matter candidates with masses of between 1 GeV and 200 GeV+, and on the order of 10-40 for tensor dark matter candidates with masses of 1 GeV to 10 GeV, and as weak as 10-38 for dark matter candidates up to about 500 GeV. The LUX direct dark matter detection experiment imposes even stronger limitations on the cross-section of interaction of scalar dark matter candidates with masses of 10 GeV to 200 GeV+ of less than 10-44.
Furthermore, multiple lines of observational evidence strongly disfavor "cold dark matter" models. Models with particles with more than 200 GeV masses are particularly strongly disfavored.
Thus, any scalar or tensor dark matter candidates must have interactions with ordinary matter than are many order of magnitude weaker than the slight interactions of neutrinos with other forms of ordinary matter.
Realistically, if scalar or tensor dark matter exists at all, it doesn't interact at all with particles outside the dark sector. In all likelihood, they simply don't exist at all, because if they interacted with other dark matter particles that had higher cross-sections of interaction, you would at least see indirect evidence of their existence as they couple to other forms of dark matter with higher cross-sections of interaction with the Standard Model.
Now, in fairness, almost nobody in the astronomy community is seriously proposing massive scalar or tensor dark matter candidates, and in the most popular models that have a boson in the dark sector, self-interacting cold dark matter models, the typical candidate, sometimes called a "dark photon" is a vector boson (i.e. spin-1) with a mass of around 100 MeV (about ten times lighter than the low end of the scale proposed by ATLAS in this experiment).
So, while this ATLAS result ruled out one subtype of conceivable dark matter, it didn't do much to rule out the leading contenders in the race to explain dark matter phenomena (e.g., light axion dark matter, keV mass scale sterile neutrino-like fermionic dark matter, and GeV mass scale fermionic dark matter such as gravitinos and the fermion partners of Standard Model bosons in SUSY theories).
But, this is a blow to SUSY, because minimal SUSY theories create a myriad of new massive scalar particles, the lightest of which are good dark matter candidates, and some non-minimal SUSY theories often also create new massive tensor particles.
In particular, all R-parity conserving SUSY theories should have one or more massive scalar dark matter candidates, and R-parity violating SUSY theories are hard pressed to explain why SUSY dark matter still exists. In R-parity violating SUSY models, one has to manipulate the SUSY model to prevent thermal relic, R-parity violating SUSY dark matter from all decaying to Standard Model particles over the life of the universe, something inconsistent with dark matter observations from astronomy.
META OBSERVATION: Since the Dispatches at Turtle Island blog was created, there have been 101 posts including this one, that address the issue of dark matter to some extent (about 15% of all of the posts at this blog). This is appropriate because dark matter is the most obvious and practically relevant of the unsolved problem in physics.