PRC passport holders who are in transit through the HKSAR to and from another country or territory may be granted a stay of seven days on each landing without the prior need to obtain an entry permit provided that usual immigration requirements are met, including possession of valid entry facilities for the destination and confirmed onward booking for the overseas journey.

If you don't want to apply for Hong Kong entry permit, you have to book a flight ticket from USA to Mainland China, Hong Kong is only a stopover place. Otherwise, you have to apply for Hong Kong entry permit.

How about if Chinese passport holder with GC of US travel to Japan but need to stay in HK for 2-3 days. Do HK request Chinese passport holder a entry permit still?

Thanks!

You don't as long as you are going to a third country and your time in HK does not exceed 7 days. Whether you have a GC is irrelevant as any Chinese passport holder can do so.

Also Peter's answer is incorrect. HK immigration will accept a verbal declaration that you are going to Shenzhen by land.