JEFFERSON CITY • As a newly minted state lawmaker from St. Louis in 1993, Joan Bray was in Missouri’s House of Representatives when an envelope containing a $1,000 campaign contribution landed on her desk.

It was an eye-opening moment.

“I was so stunned. I didn’t know what to do,” said Bray, a Democrat who would go on to serve in the Missouri House and Senate for 16 years.

The man who distributed the campaign contribution to her and other lawmakers was House Speaker Bob Griffin, who, in the era before Missouri imposed term limits on lawmakers, became the longest-serving speaker of the House.

Just three years after serving as the conduit for onsite campaign contributions in the Capitol, Griffin, a Democrat, would be found guilty in federal court of taking kickbacks from an associate in exchange for using his influence to get her lobbying contracts.

For Bray, the episode was an example of how money aimed at influencing votes can flow through the Missouri Capitol when lawmakers are in town...