  In the article The third homology of $SL_{2}(\mathbb{Q})$, Hutchinson
determined the structure of
$H_{3}\left(\mathrm{SL}_{2}(\mathbb{Q}),\mathbb{Z}\left[\frac{1}{2}\right]\right)$
by expressing it in terms of $K_{3}^{\mathrm{ind}}(\mathbb{Q})\cong
\mathbb{Z}/24$ and the scissor congruence group of the residue field
$\mathbb{F}_{p}$ with $p$ a prime number. In this paper, we develop further the
properties of the refined scissors congruence group in order to extend this
result to the case of imaginary quadratic number fields whose ring of integers
is a Euclidean domain with respect to the norm.
