Ignoring all books and Extended Universe stuff, which isn't canon anymore anyways, and possibly the few other canon things like comics, and sticking solely with the movies.
Han Solo famously said 'parsec' at some point in his life.
Which is defined in this galaxy as:
One parsec is the distance at which one astronomical unit subtends an angle of one arcsecond. A parsec is equivalent to 3.26 light years, and since a light year is the distance light travels in 1 year 9.4 trillion km, 1 parsec equals 30.8 trillion km.
So assuming that Han is one with the great and mighty metric system and the rest of the galaxy is too and their definition of a parsec is the same as our own and doesn't use average gerbil penis' as a base unit of measurement.
On top of this, there is from the script of Star Wars: A New Hope the description of the exhaust port for the Death Star and wamp rats being described by Dodonna and Luke:
The approach will not be easy. You
are required to maneuver straight
down this trench and skim the surface
to this point. The target area is
only two meters wide. It's a small
thermal exhaust port, right below
the main port. The shaft leads
directly to the reactor system. A
precise hit will start a chain
reaction which should destroy the
It's not impossible. I used to bull's-
eye womp rats in my T-sixteen back
home. They're not much bigger than
Then we can say that metric the definitive measurement system, unless there is a another quote of measurement of a different unit system from the films, I am aware of no other character specifically mentioning any other SI base unit or any other, other system.