|Owner:||United Federation of Planets|
According to the Star Trek Encyclopedia (2nd ed., p. 513), the USS Tolstoy was a Rigel-class (Rigel class at Memory Beta, the wiki for licensed Star Trek works) starship, with the registry NCC-62095. The Encyclopedia notes that the ship was named after famed Earth author, Leo Tolstoy. Startrek.com identifies the model that was labeled as USS Princeton as the Tolstoy,  and identifies the reused Constitution-class saucer model wreck as the USS Princeton. 
Originally however the ship that would become USS Tolstoy was scripted as the USS Chekov. A Springfield-class filming model with the name USS Chekov was seen on screen. A last minute post-production change resulted in Chekov being replaced with Tolstoy in the dialog, as to avoid a reference to the original series character Pavel Chekov, deemed too "cute" for the moment in TNG: "The Best of Both Worlds, Part II". The Tolstoy's designation as Rigel-class was a later invention by Michael Okuda for the Encyclopedia, to remedy the discrepancy. At the time of filming of the episode the class designation was not in use as he remembered,"Rigel: I don't think we ever came up with a ship design specifically tied to that name."
It is unclear if the renaming at the time meant that the Chekov filming model was intended to represent the Tolstoy or that a reference was made to another ship not seen in the episode, though Okuda apparently proceeded eventually from the former assumption. He himself reinforced that notion when he gave a screen-used piece of wreckage he owned, in consignment to the Propworx's Star Trek auction of 4 June 2011, described as, "Irregular piece of the saucer section of the U.S.S. Chekov from the "starship graveyard" scene in the Star Trek: The Next Generation episode "The Best of Both Worlds, Part. II."" (Propworx Star Trek auction catalog, page 44) The piece, Lot 42, estimated at $100-$200 sold for $400.
According to the Star Trek: New Frontier short story, "Performance Appraisal" in No Limits, Captain Christine Parsons (Christine Parsons at Memory Beta, the wiki for licensed Star Trek works) took command of the Tolstoy in 2366.
The Price of Freedom, sourcebook, describes the Tolstoy as a heavy scout with a crew of 90. It had 6 decks and was 215 meters in length. The ship had a maximum speed of warp factor 9.2. The ship was armed with type VII phaser emitters, and two torpedo launchers with a normal loadout of 75 photon torpedoes.