  We report on submillimetre bolometer observations of the isolated neutron
star RX J1856.5--3754 using the LABOCA bolometer array on the Atacama
Pathfinder Experiment (APEX) Telescope. No cold dust continuum emission peak at
the position of RX J1856.5--3754 was detected. The 3 sigma flux density upper
limit of 5 mJy translates into a cold dust mass limit of a few earth masses. We
use the new submillimetre limit, together with a previously obtained H-band
limit, to constrain the presence of a gaseous, circumpulsar disc. Adopting a
simple irradiated-disc model, we obtain a mass accretion limit of dM/dt less
than 10^{14} g/s, and a maximum outer disc radius of around 10^{14} cm. By
examining the projected proper motion of RX J1856.5--3754, we speculate about a
possible encounter of the neutron star with a dense fragment of the CrA
molecular cloud a few thousand years ago.
