These are a couple of references that I found to "little K" in books that I have. I hope they help.
This what the book Nicholas & Alexandra: The Last Imperial Family of Tsarist Russia (the N&A exhibition catalog book) says on the matter, for you to judge for yourself (pgs. 270-71):
"Nicholas met Matilda Kshessinskaya in March 1890 at the graduation day of the Imperial Ballet School. The love affair with 'Malechka' reached its culmination in the winter of 1892-3. The tsarevich would often visit the lively, enchanting little ballerina at home, sometimes staying the night. The affair was broken off by Nicholas a few months before his engagement."
Nicholas's diary, 1 April 1892: "I've noticed something very strange within myself: I never thought that two identical feelings, two loves could co-exist within the heart. I have loved Alix H for three years already and constantly cherish the hope that, God willing, one day I will marry her! The following winter I fell madly in love with Olga D[olgorukaya], though now that has passed! And since the summer camp of 1890 I have been passionately in love (platonically) with little K[shessinskaya]."
25 January 1893: "In the evening I dashed off to see my M.K. [Matilda Kshessinskaya], and spent a wonderful evening with her. I am completely under her spell - the pen is trembling in my hand!"
The Romanovs: Love, Power, and Tragedy has this to say about the topic on pg. 36:
"Nikolai met her in the spring of 1890, when the Imperial family graced the graduation performance of the theatrical school with their presence. The best dancer in the graduation class was seventeen year old Mathilde." Nicholas later declared in his diary, "I positively like Kschessinska." The book goes on to say that "They did not see much of each other at first, and close relations between them would inflame after his return from his cruise. The romance though, did not prove a lasting one. She was consoled by Nikolai's cousin Grand Duke Sergei Mikhailovitch and later she lived with another of his cousins Grand Duke Andrei Vladimirovitch, they had a son in 1902 and married in Cannes in 1921. "