  We show that the sign of the Euler characteristic of an $S$-arithmetic
subgroup of a simple $k$-group over a number field $k$ depends on the
$S$-congruence completion only. Consequently, the sign is a profinite invariant
for such $S$-arithmetic groups with the congruence subgroup property. This
generalizes previous work of the first author with Kionke-Raimbault-Sauer.
