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 now as much as investors demand from New Jersey, which is also struggling with an underfunded pension system. Connecticut’s net...