Im a CNA and an EMT. CNA and EMT are two totally different jobs with totally different training. About the only similiarities are both learn to take vital signs. There is no bridge that im aware of, going either way. If you want to be an EMT, you have to go to EMT school and pass the National registry exam, regardless of if you are a CNA, or for that matter an RN(I could be wrong about the RN in some states). You may be able to work as a patient care tech with only your EMT license, but most hospitals probably prefer, or require you also be a CNA, with the exception of Emergency room techs.
Fortunately neither EMT training nor CNA training takes very long or is very expensive. My EMT training took 5 months and cost a thousand bucks. My CNA training took 2 months and cost a thousand bucks. The training is similiar only in that both are hands on, feature clinicals(Ambulance and ER for EMT, usually LTC for CNA) and you have to pass a practical skills test for both.
Being a CNA probably helps make you a better EMT, since so many EMS calls involve elderly patients, but being an EMT probably has little value working as a CNA, since you will almost never get to practice most EMT skills in a LTC setting, or even hospital setting, unless you work in an ER. If in the rare situation a patient or resident falls and breaks their hip or something, you will at least be johnny on the spot with the spine board lol.