With the resistor in parallel, you are creating a [u]voltage divider[/u] where one of the "resistors" is the internal resistance of the piezo device. Yes, that will reduce the voltage. Since the piezo (unlike most voltage sources) has high source-impedance, a high-value resistor in parallel will reduce the voltage.
A resistor in series with the Arduino input will also create a 3-way voltage divider where the voltage is divided between the piezo, the resistor, and the Arduino. However, since the Arduino has an input impedance of around 100M, almost all of the voltage will be "dropped" across the Arduino input, and the series resistor will have little effect.
Normally, you'd use two resistors to make a regular voltage divider and you could calculate the voltage drop. With the piezo as one of the "resistors", we don't know the internal impedance of the piezo, so we can't calculate the voltage drop. (I believe it's capacitive, rather than resistive.) But, if you want to experiment, a single parallel-resistor is fine.
BTW - You have an unknown and uncontrolled voltage which will go positive and negative. I'm not sure what voltage you are getting, but the Arduino is limited to 0-5V. Any negative signal, or any signal above 5V can damage the Arduino. So, I recommend that you use a pair of [u]protection diodes[/u].