it is "доверяй, но проверяй" or "doveriai, no proveriai" or, in cognates, "toware, now forware". Translates to: "trust, but check" with each verb in second person singular imperative. During the cold war era it was popular amongst Americans either as a way to deride Soviet authorities as village morons or simply because they didn't care to update their studybooks for Russians since the 19th century in the United States of America. The first result in google for contemporary usage goes like: "you trust, but you verify, to quote Ronald Reagan." Is joke because it is actually just an outmoded Russian proverb.

To Russians watching Raegan doing it over and over was as if someone was talking like this to the Americans:

"Or as you say in America, [dramatic pause] [strong accent] 'If you trust before you try, you may repent before you die.' [facial expression as if he had just said something profound]."

Likely made famous over here

It first became widespread in English when Ronald Reagan used it in reference to signing a nuclear arms treaty with the Soviet Union.