What type of osomosis does tap water have?

Osmosis is the diffusion of water molecules. You may be thinking about the filtration method termed "reverse osmosis". The movement of water depends on the difference in solute concentration ocross a selectively permeable (lets water in/out) membrane. So the osmosis of tap water depends on its solute concentration relative to the other side of a membrane. In general, water moves from areas of high concentration to low concentration. This is why cabbage wilts when placed in salty water (more solutes in salty water means lower concentration of fresh water relative to the plant cells, so water leaves the cabbage as the cells become flaccid).