Courts have wide discretion to determine how they run themselves. Johnson v. Perry, 20 Wn. App. 696, 582 P.2d 886 (1978). The case Scavenius v. Manchester Port Dist., 2 Wn. App. 126, 129-30, 467 P.2d 372 (1970), interprets CR 38 and 39 to vest discretion in the trial court in deciding whether a jury trial should be granted.
Under Const. art. 1, 21, the right of trial by jury shall remain inviolate. That right includes the right to jury trial in criminal cases (STATE v. PRICE, 59 Wn.2d 788, 370 P.2d 979 (1962); 47 Am. Jur. 2d JURY 51 (1969)). In civil cases, a jury is available if a statute so provides or if the matter is one which was triable before a jury when the constitution was adopted. IN RE ELLERN, 23 Wn.2d 219, 160 P.2d 639 (1945).
In Re Marriage of Firchau, 88 Wn.2d 109, 558 P.2d 194 (1977) held that a court had the authority in a family law case to deny a demand for a jury trial.
Green v. Hooper, 149 Wn. App. 627 (2009) said the courts can deny motions for jury trials in cases of equity (not law).
The court in Johnson v. Perry, 20 Wn. App. 696, 582 P.2d 886 (1978) (http://www.mrsc.org/wa/courts/index_dtSearch.html) said the following:
" The case SCAVENIUS v. MANCHESTER PORT DIST., 2 Wn. App. 126, 129-30, 467 P.2d 372 (1970), interpretsCR 38 and 39 to vest discretion in the trial court in deciding whether a jury trial should be granted.
" We hold that the only effect of the adoption of CR 38 and 39 is to vest in the trial court wide discretion in cases involving both legal and equitable issues, to allow a jury on some, none, or all issues presented.
Subsection (c) of CR 39 allows an advisory jury on equitable issues in the discretion of the trial court.
Such discretion should be exercised with reference to many factors including, but not necessarily limited to the following: (1) who seeks the equitable relief; (2) is the person seeking the equitable relief also demanding trial of the issues to the jury; (3) are the main issues primarily legal or equitable in their nature; (4) do the equitable issues present complexities in the trial which will affect the orderly determination of such issues by a jury; (5) are the equitable and legal issues easily separable; (6) in the exercise of such discretion, great weight should be given to the constitutional right of trial by jury and if the nature of the action is doubtful, a jury trial should be allowed; (7) the trial court should go beyond the pleadings to ascertain the real issues in dispute before making the determination as to whether or not a jury trial should be granted on all or part of such issues."
RCW 2.08.010 grants jurisdiction to the Superior Court.
RCW 4.40.060 Trial of certain issues of fact--Jury. An issue of fact, in an action for the recovery of money only, or of specific real or personal property shall be tried by a jury, unless a jury is waived, as provided by law, or a reference ordered, as provided by statute relating to referees. [1893 c 127 § 33; Code 1881 § 204; 1877 p 42 § 208; 1873 p 52 § 206; 1869 p 50 § 208; 1854 p 164 § 183; RRS § 314.]
RCW 4.40.070 Trial of other issues of fact. Every other issue of fact shall be tried by the court, subject, however, to the right of the parties to consent, or of the court to order, that the whole issue, or any specific question of fact involved therein, be tried by a jury, or referred. [1893 c 127 § 34; RRS § 315.]
So, technically, you can demand a jury trial, or make a motion for a jury trial, but a judge would almost certainly deny your motion because that's the way they do things.
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By statute the procedure in Washington for termination of parental rights is goverened by RCW 13.34.190. I have included the link for you to read it on line. It references the 'fact finding' hearing that takes place before the judge. It is the judge who then enters findings of fact and the ensuing order. I suggest you also look at RCW 13.34.110 and RCW 13.34.130. http://apps.leg.wa.gov/RCW/default.aspx?cite=13.34