Am I allowed to return home after being releases from class ?

PFC Dominic Pfc Let me put it this way..... It should have been laid out to you in advance by your first line supervisor.

My way was.... If you checked in after class the first day, Id tell you next time just let me know your done and headed home.
If you did not check in after class the first day, then you would be standing in the daily close out formation for the rest of your class days.
For me, doing the right thing, being personally responsible was rewarded..
Attempting to be a shammer was also rewarded...... with more work.

Normally, when you're taking a course like CLS, Field Sanitation, Unit Armorer, etc. and you're released for the day, then your duty day is done. The CLS class is your place of duty for the day.

A counter-question is: Can you find something stating that you don't have to return to the office?

TL;DR: Your unit/office is always your default place of duty unless directed otherwise by classes, TDY, or any other events directed by your unit. The safest option is to ask your NCO what he or she expects of you in the event of daily early release. There's a part of the NCO creed that says, "I will communicate consistently with my Soldiers and never leave them uninformed." There's no reason this can't work both ways. Two way communication builds trust and confidence. A simple phone call of "SGT, we just got released early from the class at 1600. Do you need anything from me, or do you mind if I head back to my room to study today's/tomorrow's material?"

Additional insight:
Normally, if I send one of my Soldiers to a class of some sort, I (and most leaders) consider them on the classes schedule (whether early or late) until the class is complete. If the class lets out early for one day, I don't mind if they go home. I expect them to manage themselves and their schedules like adults for the duration of the class. If the class is nearby, there are times when I've asked them to drop by the office either during lunch or after they've been released for the day, to take care of items that are specific to them (finance, leave form, prior submitted documents that need error corrections). Outside of that, the class is their place of duty, so reporting and departing from class temporarily takes the place of reporting and departing from the unit area.

The thing is, your direct leadership will dictate when and where you are supposed to be. It doesn't need to be in writing. Some classes only control the student schedule specifically during the course hours; meaning, the class expects students to do morning formation and PT with their units, and report back to their units at the end of each day. That said, a school or class attendance takes higher priority over most other things, because of the time, money, and personnel already allocated to it by the unit. The best practice is not to do anything crazy between your early release time and close of business. If you're 21 and over, don't start drinking and then decide to walk through your unit area at 1630 in civilian clothes while intoxicated (it sounds silly, but it happens). While you might rightly be on an early release, it can still show a lapse of judgement, which could lead to mandated reporting to the unit after each day of training.