This type of question keeps arising in almost all establishments, no matter how big or small they may be. As an HR Head, you understand the hierarchy of your company, who reports to whom. Much will depend on your cadres, salary, levels/grades, etc. You are in two different cadres. One should not develop a mindset of who is superior or inferior. It's important that HR maintains a good working relationship on a day-to-day basis.
There may be occasions where there is a conflict between colleagues working in different streams, mainly egoistic, like "I'm superior, senior," etc. Especially HR sometimes carries a grudge against others and tries to do whatever is possible to bring disrepute to the other, putting spokes in their career path, spoiling their chances, etc., misusing a free approach with the CEO, COO, etc. HR should keep in mind a basic thing: they are in support services to the production team and should do everything possible to maintain a cool, cordial relationship with others. No production, no revenue, no pay, no company can exist. Some may even threaten with dire consequences. That approach is not good for the organization. An affronted HR team is never desired.