Using a content class with a 'selection' field, a search can be performed with the Field Criterion:

$query = new Query();
$query->criterion = new Criterion\Field( 'selection_single', Criterion\Operator::EQ, $valueIndex );

However, it the selection type is 'Multiple choice', this search criterion does not work (no results are returned).

It seems that it is possible to query only by the first option using the 'IN' operator:

$query = new Query();
$query->criterion = new Criterion\Field( 'selection_multiple', Criterion\Operator::IN, array( (int)$valueIndex) );