Fla. Stat. § 682.19

Any application under this law may be made to the court of the county in which the other party to the agreement or provision for arbitration resides or has a place of business, or, if she or he has no residence or place of business in this state, then to the court of any county. All applications under this law subsequent to an initial application shall be made to the court hearing the initial application unless it shall order otherwise.