  Context. Abridged. Many stars are members of binary systems. During early
phases when the stars are surrounded by discs, the binary orbit and disc
midplane may be mutually inclined. The discs around T Tauri stars will become
mildly warped and undergo solid body precession around the angular momentum
vector of the binary system. It is unclear how planetesimals in such a disc
will evolve and affect planet formation. Aims. We investigate the dynamics of
planetesimals embedded in discs that are perturbed by a binary companion on a
circular, inclined orbit. We examine collisional velocities of the
planetesimals to determine when they can grow through accretion. We vary the
binary inclination, binary separation, D, disc mass, and planetesimal radius.
Our standard model has D=60 AU, inclination=45 deg, and a disc mass equivalent
to the MMSN. Methods. We use a 3D hydrodynamics code to model the disc.
Planetesimals are test particles which experience gas drag, the gravitational
force of the disc, the companion star gravity. Planetesimal orbit crossing
events are detected and used to estimate collisional velocities. Results. For
binary systems with modest inclination (25 deg), disc gravity prevents
planetesimal orbits from undergoing strong differential nodal precession (which
occurs in absence of the disc), and forces planetesimals to precess with the
disc on average. For bodies of different size the orbit planes become modestly
mutually inclined, leading to collisional velocities that inhibit growth. For
larger inclinations (45 degrees), the Kozai effect operates, leading to
destructively large relative velocities. Conclusions. Planet formation via
planetesimal accretion is difficult in an inclined binary system with
parameters similar to those considered in this paper. For systems in which the
Kozai mechanism operates, the prospects for forming planets are very remote.
