You are calling the param method on an HTML::Tiny object as your test but this will always return true. Instead you should be performing a param-like test on your CGI object.

Suppose the submit input field of your form is called "foo". Then your code might be:

my $cgi = CGI->new;
if ($cgi->param ('foo') {
  # have data to process
} else {
  # no data, so print an empty form
}
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If you have an aversion to using CGI (or any of the smaller, lighter CGI modules) and want to do it by hand then you can test the 2 things you've already identified but in the outer test. eg.

if ($ENV{QUERY_STRING} || 'POST' eq $ENV{REQUEST_METHOD}) {
  # have data to process
} else {
  # no data, so print an empty form
}
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