  We investigate scalarized black holes in new massive gravity dressed by a
nonminimally coupled scalar. For this purpose, we find the Gregory-Laflamme
(GL) and tachyonic instability bounds of bald BTZ black hole expressed in terms
of $ m^2$ a massive spin-2 parameter and $\alpha$ a scalar coupling parameter
to Ricci scalar by making use of the linearized theory around black hole. On
the other hand, we obtain a solution bound of $0.161<\alpha <3/16$ for
achieving non-BTZ black holes with scalar hair analytically and a thermodynamic
bound of $1/8<\alpha <13/80$ for obtaining consistent thermodynamic quantities.
Without imposing the GL instability bound ($m^2<1/2\ell^2$), we find a very
narrow bound of $0.161<\alpha<0.1625$ which is located inside tachyonic
instability bound of $\alpha>1/8+m^2_\Phi \ell^2/6$ for obtaining scalarized
black holes where $m^2_\Phi$ is a scalar mass parameter.
