  The temperature and thickness dependencies of the in-plane anisotropic
magnetoresistance (AMR) of SmB$_6$ thin films are reported. We find that the
AMR changes sign from negative ($\rho_{||}<\rho_{\perp}$) at high temperatures
to positive ($\rho_{||}>\rho_{\perp}$) at low temperatures. The temperature,
T$_s$, at which this sign change occurs, decreases with increasing film
thickness $t$ and T$_s$ vanishes for $t$ $>$ 30 nm. We interpret our results in
the framework of a competition between two components: a negative bulk
contribution and a positive surface AMR.
