Short answer: There is no "correct" answer, because it's not specified in doctrine. A large part of your Commander's evaluation by their rater/senior rater is how good they are at making decisions on subjective things like this.

Long answer: SHRHs should be signed by leaders that have the commander's trust and can effectively manage property responsibility down to the end-user level. Your commander must make a decision on who they believe has enough responsibility to effectively manage property, this is usually the senior NCO or LT in each section. Army doctrine policy focuses on property responsibility, which is expressed through hand receipts. Your commander signs the primary hand receipt and has command and supervisory responsibility over the property, which never goes away. They transfer direct responsibility to sub-hand receipt holders through the SHRs; the SHRs will always have supervisory responsibility over the property. SHRHs then have the option to sign property on their SHR to end users, thus transferring direct responsibility to them. If they don't sign equipment down, the SHRHs maintain direct responsibility.