Its clearly mentioned on user manual/Warranty card of every Lead Acid Battery that dilute Salfuric Acid having specific gravity 1250 shud be used once the battery is new & being filled with electrolyte for the 1st time. After that deionised distaled Water shud be used to level up the electrolyte.
Try to avoid use of Tap water as its contains minerals/Ions which r not suitable for battery life & performance & same wud be the case if acidmixture is used. Regarding the water driping from condensor of split Air conditioner yes its is almost Pure H2O but the source through it dripped (drian pipes, grills etc) may add impurity in it so it shud be avoided too though atleast its better from Tap water or Mixture.
@driver_guy
Thanks for the sharing such a gr8 link.