MOSCOW—After one of Russia’s best-known bankers dropped into a coma in 1995 and died three days later, prosecutors called it a hit by criminals who sprinkled his office telephone with a poison reportedly obtained from a little-known government laboratory.

Now the U.K. says a substance known as Novichok, once made at the same laboratory, put Russian double agent Sergei Skripal and his daughter into a coma in southwestern England. U.K. Prime Minister Theresa May this week blamed Moscow for the attack, which has plunged British-Russian relations to their worst level since the Cold War.

The story of the banker’s murder underscores a central question about the latest incident: How did the attackers get hold of Novichok, a group of nerve agents developed in the Soviet Union?

The North Atlantic Treaty Organization, responding to the first known nerve-agent attack on a member state, has asked Russia to open up its entire nerve-agent program. The Russian government says it has destroyed all of the substance and that it didn’t carry out the attack.

But Moscow has never been entirely forthright about Novichok, experts say.