Many Poskim^[2] rule that the Kesuba is to be kept in the home of the wife’s mother [the husband’s mother in-law] or another trustworthy relative of the wife, or by the Rav or Beis Din.^[3] Other Poskim^[4] rule it is to be placed in the house of the couple, within the possessions of the wife, together with her belongings. Alternatively, if she trusts her husband to always safeguard the Kesuba even in a case of divorce, she may keep the Kesuba under his possession.^[5]  Practically, the Sefaradi custom is to keep the Kesuba by the wife’s mother, while the Ashkenazi custom is for the wife to keep the Kesuba in her possession. 

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[1] See Mishpat Hakesuba 7/71-78; Nitei Gavriel Nessuin 32 p.203

[2] Rashbash 320; Radbaz 4/70; Yifei Laleiv 66/3; Levushei Mordechai E.H. 49; Shulchan Haezer 8/3; Kneses Hagedola

[3] The reason: As the entire purpose of the Kesuba is to serve as an impediment against the husband wanting to divorce her, and if the Kesuba is in the house of the husband he can simply tear it up and then divorce her. Therefore it is to be kept away from the reach of the husband, in the possession of a relative who the wife trusts. [ibid]

[4] Igros Moshe E. H. 3/26

[5] If however she does not trust the husband in the event of divorce but simply believes she will never get divorced, and that is why she trusts her husband then she may not keep it in his possession. [Igros Moshe ibid]