There actually is a risk if they have shared the same tube of toothpaste. Assuming the hepatitis infected person applies the toothpaste directly to their toothbrush therefore exposing the exterior plastic on the toothpaste tube to the bristles on the toothbrush which could very well be contaminated.
Either way, if you live with someone who is infected with hepatitis C, it's probably best to get checked every 6 months or so even if there has been no direct or relatively in direct contact. Just to be on safe side. This is not something I have read this, just my own personal belief. And you should definitely be checked if you are in a relationship with somebody who has it. ( even though the risk of it being spread sexually is minimal.)
Are you saying you are concerned about sharing tooth paste or tooth brushes?
There would be no risk from using the same tube of tooth paste
If you mean they accidently used the same tooth brush yes there could be a risk as lostinmt said. But the good news is there are now highly effective medicines to treat and cure hep c. Treatment could be as simple as one pill a day fo r8 weeks and cured depending on th epersons genotype and if they have lifer damage or been treated before with the old treatments. The family member should look into getting treated and cured then no one would have to worry about accidently using the wrong tooth brush anymore
According to the CDC website, it is a less common risk for infection (along with nail clippers etc...) But he or she should probably get tested just to be sure. If this has happened before or if they have come in direct contact with blood, they should be tested now. Otherwise wait about 2 months. And if that test is negative, they should have another in the next few months.
Best wishes, it is probably unlikely but better safe than sorry. Wishing everyone involved the best!