Montana wants the court to rule that Wyoming is using too much water from the Tongue and Powder Rivers, while Montana residents are not getting enough water in some dry years.
Disputes between states often are decided by the Supreme Court.
The disagreement is over the Yellowstone River Compact, an agreement the states and North Dakota signed in 1950 spelling out how to share water.
Montana argues the compact should require Wyoming to limit water use — including from groundwater pumping. Montana argues that coal-bed methane production in Wyoming, which requires pumping huge quantities of groundwater, makes the situation worse.
Wyoming says in response that Montana has failed to show it has been harmed by Wyoming's water use, which is in line with the 1950 agreement.