If charges were dropped by the victim, can the state still use their written statement for evidence?

No, unless there is some exception to the hearsay rule that applies.

Most importantly, there is a confrontation clause issue.  You have a right to cross-examine any witness that is giving testimony against you.

Wherefore, unless you made admissions, the case should be dismissed.

Note, thr prosecutor will usually subpoena the witness. That means, the witness/victim will subject themselves to criminal prosecution for ignoring the subpoena.

Hope this helps