You need to test the file, not the file handle.

my $file = 'input2.txt';
print "baba baba baba baba TEXTFILE!!!\n\n\n" if -T $file;

# If you still want to read it, open the file handle and enjoy
open my $fh, '<', $file or die "Can't open $file to read: $!\n";

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Update

As hdb points out you can file test a file handle too. The OP was probably failing to open the file and thus getting a failure on the -T. This is another case highlighting the utility of the or die pattern

Cheers,
R.

Pereant, qui ante nos nostra dixerunt!

In reply to Re: File Test operators, option -T by Random_Walk
in thread File Test operators, option -T by virtuemart2

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