Not the perfect solution, but might take you further:
Malaysia does not use UTM for surveying. The EPSG registry lists several projections valid for West Malaysia, and the Selangor state.
You will find further information on malaysian CRS at
Unfortunately, none of them really fits to your data. So it may be useful to set up your own projection.
You have a reference point in WGS84 degrees (
101.759941 East 3.145241 North) and local coordinates (
106374.634 East 96819.608 North). Make sure they are in decimal degrees and meters.
For statewide surveying, Malaysia uses cassini projections, based on the GDM2000 geographic CRS. So we take the proj.4 definition of Selangor grid
+proj=cass +lat_0=3.68464905 +lon_0=101.3891079138889 +x_0=-34836.161 +y_0=56464.049 +ellps=GRS80 +units=m +no_defs
and replace the values of the origin with the known point you have:
+proj=cass +lat_0=3.145241 +lon_0=101.759941 +x_0=106374.634 +y_0=96819.608 +ellps=GRS80 +units=m +no_defs
You can use this custom projection string with PROJ.4 cs2cs, or all GDAL-based software. The reference point will be matched exactly, others may be offset, depending on the extent of your data.
If you compare a grid of this CRS (in red) with the Selangor grid (in green), you get this picture:
The Selangor grid has its true origin at some point in Kuala Lumpur (next to the Istana Budaya). Your grid has the crossing of 100000m almost on the same spot. So they have just added 100000 on both coordinates to prevent having negative and positive coordinates (a common practice in many surveying systems). So you can just subtract that value from your coordinates, and work with
If you are unsatisfied, you can try the old Kertau 1968 datum as well.
EPSG:4393 Kertau 1968 / Selangor Grid would be suitable, but is not included in all GDAL packages.
+proj=cass +lat_0=3.680344444444444 +lon_0=101.5082444444444 +x_0=-21759.438 +y_0=55960.906 +a=6377304.063 +b=6356103.038993155 +towgs84=-11,851,5,0,0,0,0 +units=m +no_defs
The additional false easting and northing of 100000 meters would be the same, since the true origin is almost on the same spot in Kuala Lumpur as for GDM2000.