Generally, in corporates and their factories, a permission slip is signed by the functional superior, who is the direct boss seen immediately. This is because he is ultimately answerable if his subordinate is missing from the workplace. However, if he lacks experience, etc., in order to avoid clashes in such circumstances, they follow something called the grade level authority. For example, only those at the Junior Manager level and above can sign, etc. Additionally, there is a further check at the security gate before allowing the individual to leave.
These permission slips, once filed, are to be forwarded, of course, finally to the HR head. The HR head will then tabulate and forward it to the concerned department if someone frequently goes out using permission slips.
I have one request based on your approach. I feel that there is an ego clash between HR and Admin. Please avoid this, at least for now, as I perceive you as very young. Kindly relax and ignore it. After all, someone will have to shoulder that risk, so why carry it until you are certain it is your duty?
Regards,
Suresh K
[Phone Number Removed For Privacy Reasons].