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This often depends greatly on the actual bank that owns the card. For some banks, additional card holders must co-sign, and therefore your credit will be built, and can be destryoed by other co-signors.
If you signed nothing, and are a cardholder by name only, then they cannot damage your credit, but you are also not building credit. The signator being the only person whose credit is affected either way.
In other words, it's all or nothing. Since you say you didn't have to sign on for it, I'd imagine that your credit is in limbo either way.
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