Perl never checks "the same directory as my script", but it usually* checks in ".".

$ cat ../script.pl
#!/usr/bin/perl
use Foo;

$ cat ../Foo.pm
print("Foo!\n");  # In same dir as script
1;

$ cat Foo.pm
print("Foo?\n");  # In current dir
1;

$ ../script.pl
Foo?
[download]

However, "." is not in @INC under -T.

$ perl -le'print for @INC'
/home/eric/lib/perl5/i486-linux-gnu-thread-multi   <-- From PERL5LIB
/home/eric/lib/perl5                               <--   environ var
/etc/perl
/usr/local/lib/perl/5.8.8
/usr/local/share/perl/5.8.8
/usr/lib/perl5
/usr/share/perl5
/usr/lib/perl/5.8
/usr/share/perl/5.8
/usr/local/lib/site_perl
.

$ perl -T -le'print for @INC'
/etc/perl
/usr/local/lib/perl/5.8.8
/usr/local/share/perl/5.8.8
/usr/lib/perl5
/usr/share/perl5
/usr/lib/perl/5.8
/usr/share/perl/5.8
/usr/local/lib/site_perl
[download]

If you don't care about this aspect of taint (i.e. if your script isn't setuid or sudo), then you can add "." to @INC explicitly by adding BEGIN { push @INC, '.' } to your script or by changing -T to -T -I. (including the ".").

$ cat Foo.pm
print("Foo!\n");
1;

$ perl -e'use Foo'
Foo!

$ perl -T -e'use Foo'
Can't locate Foo.pm in @INC (@INC contains: ...) at -e line 1.
BEGIN failed--compilation aborted at -e line 1.

$ perl -T -I. -e'use Foo'
Foo!
[download]

* — For some unspecified definition of usual.

Update: Added more examples.