one of the rare cases where smartmatch is really helpful.

Note the warning, so not meant for production code.

use strict;
use warnings;

my %fruit = (
             'apple' => ['red','green'],
             'kiwi' => 'green',
             'banana' => 'yellow',
            );

for my $search ("green","red" ){

    my @matches = grep { $search ~~ $fruit{$_} } keys %fruit;

    print "\n\n Matches for <$search> = @matches\n\n";
}
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C:/Strawberry/perl/bin\perl.exe -w d:/tmp/pm/smartmatch.pl 
Smartmatch is experimental at d:/tmp/pm/smartmatch.pl line 12.


 Matches for <green> = kiwi apple



 Matches for <red> = apple


Compilation finished at Tue Nov  9 22:04:30
[download]

UPDATE

allowed multiple matches

update

seriously, your data structure is misdesigned . If you want singular elements put them into an array too.

    my %fruit = (
                 'apple'  => ['red','green'],
                 'kiwi'   => ['green'],
                 'banana' => ['yellow'],
                );
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