  Let $\mathbf{k}$ be field of arbitrary characteristic and let $\Lambda$ be a
finite dimensional $\mathbf{k}$-algebra. From results previously obtained by
F.M Bleher and the author, it follows that if $V^\bullet$ is an object of the
bounded derived category $\mathcal{D}^b(\Lambda\textup{-mod})$ of $\Lambda$,
then $V^\bullet$ has a well-defined versal deformation ring $R(\Lambda,
V^\bullet)$, which is complete local commutative Noetherian
$\mathbf{k}$-algebra with residue field $\mathbf{k}$, and which is universal
provided that $\textup{Hom}_{\mathcal{D}^b(\Lambda\textup{-mod})}(V^\bullet,
V^\bullet)=\mathbf{k}$. Let $\mathcal{D}_\textup{sg}(\Lambda\textup{-mod})$
denote the singularity category of $\Lambda$ and assume that $V^\bullet$ is a
bounded complex whose terms are all finitely generated Gorenstein projective
left $\Lambda$-modules. In this article we prove that if
$\textup{Hom}_{\mathcal{D}_\textup{sg}(\Lambda\textup{-mod})}(V^\bullet,
V^\bullet)=\mathbf{k}$, then the versal deformation ring $R(\Lambda,
V^\bullet)$ 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 $\Lambda$-modules.
