use JSON;

$params->{timeout} = 2000;
$body->{"timeout"} = (defined $params->{timeout}?$params->{timeout} : 3000);
print "$body->{timeout}\n"; #<-----suspect line
my $body_string = to_json($body);
print "$body_string";

##</code><code>##

Output: 
2000
{"timeout":"2000"}

##</code><code>##

use JSON;

$params->{timeout} = 2000;
$body->{"timeout"} = (defined $params->{timeout}?$params->{timeout} : 3000);
my $body_string = to_json($body);
print "$body_string";

##</code><code>##

Output: 
{"timeout":2000}