In all cases of conviction, unless otherwise provided in this chapter, the judge shall enter judgment for the fine and costs against the defendant, and may commit him or her to jail until the amount of such fine and costs owing are paid, or the payment thereof be secured as provided by RCW
10.04.120. The amount of such fine and costs owing shall be computed as provided for superior court cases in RCW
10.82.030 and
10.82.040. Further proceedings therein shall be had as in like cases in the superior court: PROVIDED, That all fees, fines, forfeitures and penalties collected or assessed by a district court because of the violation of a state law shall be remitted as provided in chapter
3.62 RCW as now exists or is later amended.