  For epitaxial Sr$_3$Ru$_2$O$_7$ films grown by pulsed laser deposition, we
report a combined structural and magnetotransport study of thin films and Hall
bar devices patterned side-by-side on the same film. Structural properties of
these films are investigated using X-ray diffraction and high-resolution
transmission electron microscopy, and confirm that these films are epitaxially
oriented and nearly phase pure. For magnetic fields applied along the $c-$axis,
a positive magnetoresistance of 10% is measured for unpatterned
Sr$_3$Ru$_2$O$_7$ films, whereas for patterned Hall bar devices of channel
widths of $10$ and $5\, \mu$m, magnetoresistance values of 40% and 140% are
found, respectively. These films show switching behaviors from positive to
negative magnetoresistance that are controlled by the direction of the applied
magnetic field. The present results provide a promising route for achieving
stable epitaxial synthesis of intermediate members of correlated layered
strontium ruthenates, and for the exploration of device physics in thin films
of these compounds.

Applied Physics;Strongly Correlated Electrons