The lawsuit claims that the tech giant has used "monopolistic leverage" to generate large profits from purchases made within its own store.
It also claimed Google had bought off its competitors.
Google said that there are rival app stores for Android devices, and that apps can also be downloaded directly from developers' own websites.
The 37 states involved in the legal action include New York, Tennessee and North Carolina, as well as Washington DC.
It criticises the commission Google takes on purchases made within Google Play, which can be up to 30%, in line with Apple's App Store policies and the stores of other rivals such as Amazon and Microsoft XBox.