Star Trek Encyclopedia (2nd ed., p. 513)において、USSトルストイはライジェル級宇宙艦であり、レジストリ・ナンバーはNCC-62095となっている。名前は、地球の小説家であるレフ・トルストイに因んでいる（ただし、「トルストイ」という名の作家はレフを含めて少なくとも3人存在し、政治家の人物を含めれば4人となる）。 Startrek.comにおいては、USSプリンストンのキットをUSSトルストイとしていたが、後に訂正された。
Originally however the ship that would become USS Tolstoy was scripted as the USSChekov. A Springfield級 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.
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.