Short answer: To the extent that Desdemona becomes submissive and allows herself to be victimized, as well as her lying about the loss of the treasured handkerchief that Othello gives her, she contributes to her tragic end.
It is so often one of the great ironies of marriages that what first attracts people to one another and leads to their engagement and wedding often becomes the same element that effects the undoing of those marriages. Desdemona's attraction to the great warrior who tells her exciting tales of battle excites her to a desire to be part of his life. He, in turn, may well be attracted by her fierce independence in her conviction to marry him against the social prejudices of her Venetian society, as well as her allegiance to him when she speaks to her father who demands her obedience:
I am hitherto your daughter. But here’s my husband.
And so much duty as my mother showed
To you, preferring you before her father,
So much I challenge that I may profess
Due to the Moor my lord. (1.3.186-190)
It would seem, however, that Desdemona's independence does not last, either because she has been merely affected by the warrior spirit of her husband in the newness of their marriage and she simply imitates him in her defiance of her father, or because she changes, feeling that she must assume the more traditional role of wife lest her assertion of independence enrage him or estrange her from him. For, as the drama progresses, Othello transfers some of his bellicose nature to their personal relationship. His wife's growing submission, unfortunately, seems to contribute to his behavior and to Desdemona's demise. While Othello's jealousy certainly absorbs his ability to think clearly, Desdemona may also ignite the flames of his aggressiveness by her submissive attitude as he loses respect for her.
Further, with the villain Iago's planting of seeds of doubt and jealousy in Othello, in his irrational emotion, Othello stifles his wife's speech which has been Desdemona's most powerful weapon. It is, again, her succumbing to his overbearance that is her undoing since a change in character often causes people to become suspicious. Even when Emilia scolds her, Desdemona exhibits this new passivity,
EMILIA. Here's a change, indeed,
DESDEMONA. 'Tis meet I should be used so, very meet.
How have I been behaved that he might stick.
The small'st opinion on my least misuse. (4.2.111-114)
Having lied about her lost handkerchief that Othello has given her may also be a cause of Desdemona's undoing as it is this lie that convinces him of her guilt since Iago produces an imitation which convinces Othello that Desdemona has lost it. After this discovery, Othello allows his warrior nature to overpower him, and he kills his beautiful wife. Even in death, Desdemona once so independent and strong, surrenders and blames herself for Othello's cruelty.
Tragically, in the end, both Othello and Desdemona pervert their assets of confidence and independence and candor, destroying the love and respect which began their marriage.