Typically, Zhong Kui would be holding a Seven Star Sword or the Qixing Jian. The sword would have seven dots or seven inlaid precious stones arranged either in a straight line but more commonly in the form of the Big Dipper Constellation. Also known as the Dipper Sword, this sword is used for exorcism rituals and to drive away evil spirits. It is for this reason why you will see ceremonial or decorative Jians marked with seven stars arranged in the Big Dipper.
There is a Katana, or to be more precise, a Chokuto, in the Shitenno-Ji Temple in Osaka that's considered a National Treasure. The sword is straight, has inlays that depict cloud markings and the Big Dipper, referred to as the Shichiseiken. Sword is considered to be non-Japanese in origin and likely dates to the 7th Century.
You will see references in anime and games about the Seven Star Sword or Qixing Jian or the Shichiseiken.
Why the Taoist fixation towards the Big Dipper, I am not too sure.