There is ample evidence of Dake's involvement with the Earps (or his use of them for his purposes, depending on one's perspective) in the National Archives records of the Justice Department (both the U. S. Marshals' records and the Attorney General's records). These records are available on microfilm. There are also relevant records from the State Department records (because of Mexico's involvement in the "Cow-Boy War.")
Some of the records may be seen in Don Taylor's THE UNITED STATES OF AMERICAN V THE "COWBOYS," Tombstone: Old West Publishing Co., 2006. This volume reproduces some of the documents.
Other secondary works relevant to the subject include:
Larry D. Ball, "Frontier Lawman: Crawley P. Dake and Law Enforcement on the Southwestern Frontier," THE JOURNAL OF ARIZONA HISTORY (Autumn, 1973)
Larry D. Ball, THE UNITED STATES MARSHALS OF NEW MEXICO AND ARIZONA TERRITORIES, 1846-1912 (1978).
Stephen Cresswell, MOROMONS, COWBOYS, MOONSHINERS & KLANSMEN: FEDERAL LAW ENFOIRCEMENT IN THE SOUTH & WEST, 1870-1893 (1991).
Katherine Benton-Cohen, BORDERLINE AMERICANS: RACIAL DIVISION AND LABOR WAR IN THE ARIZONA BORDERLANDS ((2009).
These works are less concerned with the Earps and concentrate more on federal law enforcement. Ball is especially important with respect to Dake.
I might also refer you to my Doc book, p. 493, note 135, which refers to the visit of Congressional Delegate Curtis C. Bean with Wyatt Earp in Aspen Colorado in September 1885, concerning his dealings with Marshal Dake. This was during the time that Leigh Chalmers, a special investigator for the Justice Department, was reviewing Dake's accounts.
There's little doubt that Dake supported the Earps, as did Wells, Fargo, and a number of businessmen in Tombstone. They may not have approved Earp's methods (one by one), but they were not unhappy with the results. After the fact, they may have distanced themselves with what happened for political reasons, but they privately approved what had happened.
Lynn Bailey has a book forthcoming on the Cow-Boys which I fully expect to broaden our knowledge considerably.
Best!