Sorry for the zombie bump, but wanted to post the solution for any other future searchers coming here to turn off autocomplete/autofill on a New Ticket form.
Within "include/class.forms.php", in the class "TextboxWidget" block (line 4382), change
<input type="<?php echo $type; ?>"
to <input autocomplete="none" type="<?php echo $type; ?>"
and in the class "TextareaWidget" block (line 4471) change
<textarea <?php echo Format::array_implode('=', ' ',
to <textarea autocomplete="none" <?php echo Format::array_implode('=', ' ',
I used "none" instead of "off" because I read there are some issues with chrome and the autocomplete "off" flag that I didn't verify. I only needed it turned off with Short Answer and Long Answer fields, but you should be able to make the same changes to the other classes if you need.
This was done in the current version v1.17.2 but this is the only thread I found through Google where someone asked this question.