Is it safe to connect an Arduino to the human body?
It's not advisable unless the entire project is low voltage and battery operated.  Anything mains operated could be dangerous even if transformer isolated.  There are specific safety requirements for mains operated patient attached equipment to protect against excessive leakage currents and potential safety hazards due to equipment or component failures.  

Those regulations apply to professional medical equipment, but they are there for a reason.  You shouldn't assume that it's safe to ignore them even if it's just a hobby project.