(CNN) Florida voters are almost evenly split on both the state's Senate and gubernatorial contests, while the Senate contest in Tennessee appears to be shifting in the Republican's favor, according to new CNN polls conducted by SSRS.

In Florida's Senate race, Bill Nelson is locked in a close race with Rick Scott, with 49% of likely voters supporting Nelson, the incumbent Democrat, and 47% behind Scott, the state's Republican governor. The gubernatorial race is similarly divided: 49% for Democrat Andrew Gillum and 48% for Republican Ron DeSantis. In both contests, the share of likely voters who say they could change their minds in the final days of the campaign stands in single digits.

The results reflect tighter contests than CNN's last poll in the state, which found both Democrats with an advantage. An average of other recent polling on each of the Florida races suggests a narrow Democratic tilt. A CNN poll of polls average assessing five recent live-interviewer telephone polls of the race -- including the new one from CNN -- finds Nelson topping Scott 48% to 45%, while Gillum edges DeSantis 49% to 45%.

In the new CNN poll, the decline in support for Gillum comes across demographic groups, but is sharpest among non-white voters (Gillum drops nine points among that group), those without college degrees (down seven points) and women (down six).

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