Painleve singularity analysis is applied to a simple model for charged
particle motion in magnetic reconnection regions. We identify two fie
ld geometries for which test-particle motion is integrable; i.e. there
exists a complete set of isolating integrals: the neutral sheet confi
guration and the circular O-line magnetic field. Both of these systems
are solvable in terms of the second Painleve transcendent. An infinit
e set of weak Painleve candidates is also discussed.