The Republican presidential candidate Rand Paul is leading Hillary Clinton in a pair of key swing states, according to a poll released on Thursday.

The survey, conducted by Quinnipiac University, finds Paul ahead of Clinton by three percentage points in Colorado, at 44% to 41%, and by one point in Iowa, at 43% to 42%.

Several recent surveys have shown that Clinton's advantage is waning in a number of such battleground states.

Clinton, who is expected to declare her candidacy in the coming weeks, "has lost ground in almost every matchup in Colorado and Iowa since an 18 February Swing State [poll]," the Quinnipiac poll states. Voters in each state said the former secretary of state was not honest and trustworthy – an issue that has especially dogged Clinton since it was revealed she used a private email server while serving as secretary of state in the Obama administration.

Paul, who formally launched his presidential campaign on Tuesday, plans to attack Clinton's character and zero in on her honesty. Other GOP presidential contenders have also seized on the recent email controversy, as well as the identity of donors to the Clinton Foundation, to raise questions about Clinton's integrity.

Peter A Brown, the assistant director of the Quinnipiac poll, said the new numbers were a significant boost for Paul and particularly damaging for Clinton, who is now effectively tied with every Republican candidate in hypothetical swing state match-ups.