15. If $x^{2}-2(k+1) x+4$ is a perfect square, then the value of $k$ is ( ).
(A) $\pm 1$
(B) $\pm 3$
(C) -1 or 3
(D) 1 or -3
15. D.

Let $x=k+1$, then $4-(k+1)^{2}$ is a perfect square, so $4-(k+1)^{2}=0,1,4$.
Solving gives $k=-3,1,-1$.
Upon verification, $k=-3,1$ meet the requirements.