Home insurance carriers will often times have an "excluded dog breed" list. This list will exclude coverage for certain breeds of dogs. While there are some variances in carrier lists, the common breeds of: Pitbulls, Rottweilers, German Shepherds, Doberman Pinschers, and Huskies are often excluded.
If your dog belongs to this list and bites or attacks someone, you can be held liable for their injuries as your home insurance will deny a claim and even non-renew your policy.
If your dog does not belong to this list of excluded breeds, then your home policy will likely afford coverage and pay out any liability loss up to your home policy liability limit.