Can you work as an EMT if you have been arrested but do not have a trial yet and are therefore not formally charged?

If your employer is not aware of your felony arrest you would well advised to notify them. As far as I know, EMT's are licensed by a state certifying board, and you might find youself in violation of your oath of office if you don't notify them of your legal difficulty..

The probablity is that you may be suspended from duty until such time as the legal problems are ironed out, but if you don't notify them, you are placing your EMT certificate at risk.