Scifi - Serial killer comes back 10 or 11 times just to kill another victim. Read in 1990s.

[Guy]

Genre: Scifi, possibly scifi short story.
Plot details: It opens with a serial killer being sentenced to death, and the killer's last words before being electrocuted are that he'll come back 10? 11? times to kill again, and the protagonist / detective tries to stop him from killing again?

It's been forever since I read it at some point in the 1990s, so it was definitely published before 2000 and probably at some point after 1980.

It's been driving me nuts trying to figure out what the book was and I'd love to read it again!

[Kris]

Guy, how does the serial killer come back to live? Spoilers are okay - just give us a clear warning before revealing a spoiler.

What do the victims have in common?

What is the story's time period and location?