Chase H.Q. was successful enough to earn two arcade-based sequels - the widely released Special Criminal Investigation released in 1989 and the extremely rare Super Chase: Criminal Termination released in 1992.
The 1997 PlayStation game Ray Tracers, developed and released by Taito, has been described as "more or less a follow up" to the game, with "only a few differences" such as a different speed-boost system and a greater variety of targets.
In February 2006, Chase H.Q. : Nancy Yori Kinkyuu Renraku (English: Chase H.Q. - An Urgent Call From Nancy) was presented at the Arcade Operator's Union trade show in Tokyo. The game was released as Chase H.Q. 2 later in the year.
Source: Wikipedia, "Chase H.Q.", available under the CC-BY-SA License.