There is for sure going to be a shorter more golf-ish solution, but the obvious one is:

perl -ne '@cols = split /\t/; print if $cols[1] == 0' mydat.txt
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• -n means iterate the next block of code over the supplied files one line at a time (where line means whatever is separated by the value of $/ which is the newline of your platform by default). The text line is presented in the variable $_ with a newline.
• -e means interpret the next commandline argument as a chunk of code.
• Many builtins, such as split, print and // regex matching, operate on $_ by default if no string/list argument is given.