Do not use poison if you care about your dog. The modern version of Warfarin is deadly to dogs. Even if the dog does not get to the poison baits, it could prey on a mouse or rat which is slowed from being poisoned. In addition wild predators and scavengers can be poisoned by consuming poisoned rodents.
Use snap traps put inside enclosure boxes designed for that purpose. I use these JT Eaton No. 401 snap trap station and I use the TomCat rat snap traps. In Dallas TX we don't have mice, but do have rats. Juvenile rats are small and could be mistaken for mice, but mice are much smaller. My brother in rural MA has mice.
I have very successfully used these devices on rats outside around the perimeter of the house and under bird feeders in the yard. But right now I have a rat roaming the house at night and I have not been able to entice it into a trap in two weeks of trying.
EDIT SUCCESS got up at 2:30 am (30 Jan 2017) to let our elderly dog out into the backyard found an adult rat (140 g brown rat aka Norway rat Rattus norvegicus) dead in the Tomcat black plastic snap trap inside the Eaton box. These traps are much easier to set than the old Victor traps.
But two days ago, frustrated and exasperated with finding rat feces every morning in the den, I bought two of the old Victor traps and put them in another box placed adjacent to the box that had been there for a least two weeks.
I thought maybe the rat wouldn't recognize the Victor trap. These are very hard to set--I guess one has to get the procedure down. Decades ago I knew how to do it, but in handling them I failed to recognize that I had set one and was handling it set thinking it was not. It did not trip, but could have with consequences to me. If you are distracted handing an old Victor trap you can get nailed. I am sure it could break a finger. I don't want to think about what it would do to a dog's muzzle or to a child's hand.
One critical factor is to deprive an indoor rat of all food sources except what is in the traps. Before catching this rat I unloaded and pulled back a bookshelf with a recess under it. A rat had stashed a pile of dog food there. I cleaned it up and we made sure we had no dog food left in an accessible bowl overnight.