Is mass conserved in both physical and chemical changes?

The Law of Conservation of Mass states that mass is neither created nor destroyed in a chemical reaction or a physical transformation. Hence, a short answer to the question is - yes, mass is conserved whether matter undergoes a chemical change or a physical change.
Physical changes are changes that involve a simply change in phase. Condensing of a gas is an example. Any change that does not involve a change in chemical composition is physical change. Tearing up paper does not change the chemical composition of the paper, but merely changes the size of the paper. In both examples, there is no change in identity of the atoms involved, or even the general chemical composition of the paper. If it were possible to look at and track the individual molecules in the paper before and after the change, then it will be possible to see that the number of molecules did not change. 
It is less intuitive for chemical changes. Chemical changes involve a reaction a change in chemical composition. For instance, hydrogen gas can react with oxygen gas to form water. While the individual atoms are still there, the chemical composition is different. This involved a rearrangement of chemical bonds. However, it can easily be justified where the atoms went - nothing disappeared, and nothing just appeared out of nowhere - mass is neither created nor destroyed. The chemical reaction simply resulted to the rearrangement of chemical bonds. 
Hence, in both cases - physical or chemical change - the mass is conserved.