DEXTER — Steven Lake, who police say killed his estranged wife and two children then committed suicide, arrived at his family’s home armed with a 12-gauge shotgun, a 22-caliber pistol, a knife, extra ammunition and a flashlight, police said this afternoon.

Police are still searching Lake’s home but have so far have found no suicide note or written plan that might shed some light on his thought process in the days and hours before he killed his family.

Police believe Lake arrived at the house of his estranged wife Amy before dawn. There was no sign that he forced his way into the house, though it’s possible the entry of the State Police tactical team covered up signs of forced entry, said State Police spokesman Steve McCausland.

At some point in the early morning, Steven Lake used the shotgun to shoot his wife, his children and then himself.

Police still have not determined where Steven Lake obtained the shotgun he used.

“We will continue to work on getting answers but at this point, we may never have answers to some of those questions we may have,” said McCausland.