a relay question

I have a circuit that normally runs at 3-5v and then when triggered, it gets pulled to ground (around .1-2 mv leakage). I want to use this to trigger a relay to close a different low voltage circuit. Can I use the " sainsmart DC 5V Relay Module for Arduino PIC ARM DSP AVR MSP430 TTL Logic" board to achieve this?

use the N.C. portion of the relay...when your circuit goes to ground the relay turns off and the contacts are closed...that is, If the circuit can hold open the relay....