  Contact path geometries are curved geometric structures on a contact manifold
comprising smooth families of paths modeled on the family of all isotropic
lines in the projectivization of a symplectic vector space. Locally such a
structure is equivalent to the graphs in the space of independent and depedent
variables of the family of solutions of a system of an odd number of second
order ODE's subject to a single maximally non-integrable constraint. A subclass
of contact path geometries is distinguished by the vanishing of an invariant
contact torsion. For this subclass the equivalence problem is solved by
constructing a normalized Cartan connection using the methods of
Tanaka-Morimoto-\v{C}ap-Schichl. The geometric meaning of the contact torsion
is described. If a secondary contact torsion vanishes then the locally defined
space of contact paths admits a split quaternionic contact structure (analogous
to the quaternionic contact structures studied by O. Biquard).
