Gravitational instability (GI) controls the dynamics of young massive protoplanetary discs. Apart from facilitating gas accretion on to the central protostar, it must also impact on the process of planet formation: directly through fragmentation, and indirectly through the turbulent concentration of small solids. To understand the latter process, it is essential to determine the dust dynamics in gravitoturbulent flow. For that purpose, we conduct a series of 3D shearing box simulations of coupled gas and dust, including the gas's self-gravity and scanning a range of Stokes numbers, from 10 ^-3 to ∼0.2. First, we show that the vertical settling of dust in the mid-plane is significantly impeded by gravitoturbulence, with the dust scale height roughly 0.6 times the gas scale height for centimetre grains. This is a result of the strong vertical diffusion issuing from (I) small-scale inertial-wave turbulence feeding off the GI spiral waves and (II) the larger scale vertical circulations that naturally accompany the spirals. Second, we show that at R = 50 au concentration events involving submetre particles and yielding order 1 dust-to-gas ratios are rare and last for less than an orbit. Moreover, dust concentration is less efficient in 3D than in 2D simulations. We thus conclude that GI is not especially prone to the turbulent accumulation of dust grains. Finally, the large dust scale height measured in simulations could be, in the future, compared with that of edge-on discs seen by ALMA, thus aiding detection and characterization of GI in real systems.