It depends upon what the rumor is about. If I spread a rumor that you bought yourself a Lamborghini, you selfish spoiled girl, it's easy enough for someone to eventually check that out. Just watch for all these weirdos here peeking into your garage.
If it's just a he said/she said situation, it really depends upon what's said, and how well you know the content of the character of the person spreading the rumor and/or, the person the rumor is about.