The investigators were not exactly detectives, they were similar to a group of cowboys. They were easily bribed and did not care much for their jobs.
The Osage were eventually able to get the federal government involved. The newly formed FBI was brought into the case. J Edgar Hoover, who was eager to work on the case appointed Tom White to head the investigation.
Tom white worked very hard on this case. He even had undercover agents come into the town to help him. White developed a very strong lead, and the suspects name was William Hale
However, Hale was very strategic, not to mention wealthy. He was known as the "King of the Osage". He was usually successful when he attempted to bribe his way out of situation he was stuck in.
Money, Money, Money
Finally, enough evidence was collected to bring him and Mollie's husband, Ernest to court
In the end, even after many attempts of Hale's bribing, he and Ernest were found guilty. But, not all was equal, they were not sentenced to death (even after killing dozens!), just life in prison. They were even let out several years later.