It’s getting riskier and riskier to own Connecticut debt, according to a key bond-market metric.

The extra yield that investors demand on 10-year Connecticut general-obligation bonds rose to 0.95 percentage May 17, according to data compiled by Bloomberg. That’s just shy of the all-time high of 0.96 percentage point reached last June, when state lawmakers were contending with what became a prolonged stalemate over how to close its budget deficit.

That extra yield, or spread, on Connecticut debt is...