It turned out that setting status to 206 before call of $r->send_http_header solved the problem. Here is a fixed version of code:

        my $range_request = ($mod_perl::VERSION < 1.99) ? $r->set_byte
+range : 0;
        if((my $status = $r->meets_conditions) eq OK()) {
                if ($mod_perl::VERSION < 1.99) {
                    if ($range_request) {
                        $r->status(206);
                    };
                    $r->send_http_header;
                };
        }
        else {
                return $status;
        }
        return OK() if $r->header_only;

        if($range_request) {
                while(my($offset, $length) = $r->each_byterange) {
                        $r->print(substr($contents, $offset, $length))
+;
                }
        }
        else {
                $r->print($contents);
        }
        return OK();
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