I wouldn't.
People often put on this site that demineralised water or filtered water is okay to top up tanks with - but that simply strips out salts and minerals that your fish need to live healthy lives.
It is safe to use demineralised water or filtered water AS LONG AS YOU REPLACE necessary nutrients like salts and minerals.
A water filter will remove chlorine and some of the heavy salts and scales which is fine for the fish - but things like snails and shrimp need carbonates and salts to make their shells..... fish need certain salts in the water to promote breading etc..
If you want to use filtered water, I would suggest you dont use it all the time, or you also add a water treatment/conditioner such as this:
http
/www.eshalabs.com/optima.htm
This will replace the salts lost in the water filter, and help to recreate natural water values.
Id stick to tap water unless you know that there is a problem with it.
x
...edited:
Just re-read the original post..
Your tap water softner may add salts to the water, simply preventing the effect of carbonates (e.g. limescale)
contact the supplier to see what gets added to the water, and then let us know so we can help. xx