 There is a growing literature on modal extensions of connexive logics. In Wansing 2005, the language of the connexive logic C is extended by modal operators □ and ◊ (“it is possible that”) to define a connexive and constructive analogue CK of the smallest normal modal logic K. The system CK is shown to be faithfully embeddable into QC, to be decidable, and to enjoy the disjunction property and the constructible falsity property.