Floating USART line cause uC reset
Setting a pull down in RX pin. Didnt work.


Bad idea, that would be detected as a break. Use a pullup resistor for RX, as UART signals are idle high.


  Everything was fine until I detected that putting noise (just touching BOTH lines with my hands) cause a hardware reset in the uC and the program stop working at all.


Touching signal lines with bare hands may cause ESD, and no, the MCU is not supposed to work properly in that case.