I guess you're right, it doesn't state "hard case" but it does refer to a secure container. In my non legal mind, I guess I confuse the two.
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Yeah, the instructor was adamant about it being in a locked case and out of your immediate control by placing it as far away as possible.
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The operative phrase of the law being discussed is:
shall possess the same in a vehicle unless such weapon is unloaded and contained within the locked trunk of such vehicle or in a locked case or other secure container.
Your choices are 1) locked trunk, 2) locked case, or 3) other secure container. So if you don't have a trunk, put it in a locked, hard-sided case. The law does not require that the locked case be in any particular portion of the vehicle (though putting it out of sight is not a bad idea). If you put it in a locked trunk, you don't have to put the gun inside anything, though a case is advisable to prevent damage to the gun.