Hillary ClintonHillary Diane Rodham ClintonChris Murphy’s profile rises with gun tragedies DNC, RNC step up cyber protections Gun proposal picks up GOP support MORE continues to lead a field of Republican candidates in early presidential polling of Ohio, but Sen. Rand PaulRandal (Rand) Howard PaulHouse bill set to reignite debate on warrantless surveillance Authorizing military force is necessary, but insufficient GOP feuds with outside group over analysis of tax framework MORE (R-Ky.) has narrowed the gap to 4 points. 

A new Quinnipiac poll released Thursday shows Clinton would top Paul 46 percent to 42 percent in a hypothetical general election match-up in the battleground state. 

She led by 8 percent the last time the firm polled the question in May. 

Clinton has a 52 percent favorable rating, while 43 percent view the former secretary of state unfavorably. Paul is less well-known, with 35 percent having a favorable view of him and 30 percent viewing him unfavorably. 

Clinton's favorable rating is largely unchanged in Ohio over the past few years. Her previous low came during the 2008 campaign, when 46 percent approved of her. 

Paul is the only potential GOP candidate who wins more independents than Clinton, 44 percent to 41 percent. Among women, however, she leads all Republicans by 20 points or more. 

In a match-up with former Florida Gov. Jeb Bush (R), Clinton leads 48 percent to 37 percent. She has the same margin in a potential matchup against New Jersey Gov. Chris Christie (R). 

Against Ohio Gov. John Kasich (R), she leads 47 percent to 40 percent. 

The poll surveyed 1,366 registered voters and has a margin of error of plus or minus 2.7 percent.