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Let k be field of arbitrary characteristic and let Λ be a finite dimensional k-algebra. From results previously obtained by F.M Bleher and the author, it follows that if V • is an object of the bounded derived category D b (Λ-mod) of Λ, then V • has a well-defined versal deformation ring R(Λ, V • ), which is complete local commutative Noetherian k-algebra with residue field k, and which is universal provided thatLet Dsg(Λ-mod) denote the singularity category of Λ and assume that V • is a bounded complex whose terms are all finitely generated Gorenstein projective left Λ-modules. In this article we prove that if Hom Dsg(Λ-mod) (V • , V • ) = k, then the versal deformation ring R(Λ, V • ) is universal. We also prove that certain singular equivalences of Morita type (as introduced by X. W. Chen and L. G. Sun) preserve the isomorphism class of versal deformation rings of bounded complexes whose terms are finitely generated Gorenstein projective Λ-modules.such that M = coker f 0 , and for all integers i > 0 and j ∈ Z we have Ext i Λ (ker f j , Λ) = 0. Following [1] and [4], we say that a finitely generated left Λ-module M is of Gorentein dimension zero or totally reflexive provided that the left Λ-modules M and Hom Λ (Hom Λ (M, Λ), Λ) are isomorphic, and that Ext i Λ (M, Λ) = 0 = Ext i Λ (Hom Λ (M, Λ), Λ) for all i > 0. It is well-known that finitely generated Gorenstein projective left 2010 Mathematics Subject Classification. 16G10 and 16G20 and 20C20.