In case you are also confused about there being a statute of limitations on murder in Japan: It was indeed 15 years until 2004, when it was extended to 25 years. In 2010 the statute of limitations for murder was abolished (and for other serious crimes extended from 15 to 30 years).
I don't think it's quite clear when Kindaichi's main series are set exactly, but with the stories having been published since 1992 we can expect it to be somewhere around that time (I don't know from memory if in later chapters tech appears that would seem contradictory to the period), so Mitsuya claiming that the SoL was about to end after 15 years is consistent.
