The HTTP::Tiny doc says:

verify_SSL - A boolean that indicates whether to validate the SSL certificate of an https-connection (default is false)

... By default, HTTP::Tiny does not verify server identity.

It works as expected for me, see below (note the PerlMonks SSL certificate is valid for perlmonks.pair.com, but not perlmonks.com). Could you provide an SSCCE for the problem?

$ perl -MHTTP::Tiny -le 'print HTTP::Tiny->new()->get("https://perlmon
+ks.com/")->{status};'
200
$ perl -MHTTP::Tiny -le 'print HTTP::Tiny->new()->get("https://perlmon
+ks.pair.com/")->{status};'
200
$ perl -MHTTP::Tiny -le 'print HTTP::Tiny->new(verify_SSL=>1)->get("ht
+tps://perlmonks.com/")->{status};'
599
$ perl -MHTTP::Tiny -le 'print HTTP::Tiny->new(verify_SSL=>1)->get("ht
+tps://perlmonks.pair.com/")->{status};'
200
$ perl -MHTTP::Tiny -le 'print HTTP::Tiny->new(verify_SSL=>0)->get("ht
+tps://perlmonks.com/")->{status};'
200
[download]