Federal regulators in the USA also have investigated the company over antitrust claims, but Google settled with the Federal Trade Commission in 2013 without making any major concessions on how the company runs its internet search engine.
The Kansas City Star first reported on the investigation.
Mr. Hawley said his probe was in part prompted by a record $2.7 billion fine European regulators levied against Google in June for allegedly favoring its services in its search results.
"There is strong reason to believe that Google has not been acting with the best interest of Missourians in mind", Hawley said in a statement.
Missouri's Hawley said the FTC's inaction created an opening. "However, we have strong privacy protections in place for our users and continue to operate in a highly competitive and dynamic environment", Lenihan said. In Washington, tech companies face the possibility of new, sweeping regulations that would implicate key areas of their businesses, including requirements to disclose information about online advertising and obligations to better police user-generated content.
Attorney generals of 37 states reached a $7 million settlement in 2013 over Google's unauthorized collection of Wi-Fi data through its Street View digital-mapping cars.
Hawley, a Republican who is running for the U.S. Senate, has opened his investigation as politicians on both sides of the political spectrum are becoming more critical of large tech companies in the wake of revelations that Russian state agents used social networks to try and influence the 2016 Presidential election.
Hawley noted that the FTC had chosen not to take enforcement action against Google after a 2012 investigation of its search practices.
Lastly, Hawley's office is investigating whether Google has manipulated search results to favor websites owned by Google and to demote websites that compete with Google. He said the agency essentially gave Google a "free pass".