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I am a junior faculty in one of the top-tier research US institutions. I just joined the department and hired two GRAs meanwhile. In addition, I would like to appoint one more individual in my research group who could be appointed as a research engineer/technician. His/her role would be to support my research program and assist my GRAs on their PhD work. I am wondering whether there are any legal issues/conflict of interests if he/she is one of my family members. How will the department see this recruitment?

The rules differ from country to country, university to university, and department to department.

On a practical note, I would not want to be in a supervisory role towards a family member. In that role I need to be able to make unpleasant decisions, like tell someone if (s)he did a bad job, handle complaints, or even discontinue employment. That is hard enough as is, but if it involves a family member...

Many, if not most, universities have policies that would forbid this, or require extra scrutiny.

Search your university's hiring, HR, and conflict-of-interest policies to see if they address this (it could be under "nepotism"). Even if you don't find anything forbidding it, don't go ahead yet - check with your department chair and/or HR administrators. Make sure you can make a clear case as to why your family member is qualified, and why the direct hire would be better than an open application process. Don't go ahead with the hire until you have explicit informed approval from someone who has the authority to approve it.

If the money for this position comes from an external grant, you should repeat the above steps with "university" replaced by "funding agency".

All the existing answers point in the same correct direction, but are in my opinion too mild.

This is an horrendous idea. Don't do it.

It's irrelevant whether your chair / department / university / funding source formally allows it. It does not matter if your family member is the most qualified candidate. You will run into suspicions of nepotism, which are virtually impossible to ever fully get rid of. People will talk. You don't want any of that at a place that you quite likely will spend the rest of your working career at, and you most definitely don't want any of that so early in your career and prior to getting tenure.

If your family member is qualified and in need for a job like this, strongly recommend them the next time of your colleagues is hiring for a similar role. Don't take them on yourself.

While I think the advice here and here is sound, let me make another observation. If the reason you want to hire this person is because they are a family member rather than in spite of it then it is probably a bad idea in any case, even if legal. Otherwise, it is a bit more ambiguous.

One way to avoid some, but not all, of the conflicts, if you think they are indeed the best person for the job is to see if you can defer the decision to hire to one of your superiors, say the head of the department. If your superior agrees that they should be hired, not just that they can be hired then go ahead. This won't solve the day-to-day supervision issues, nor the issue of what would occur if they had to be fired, of course.