ATLANTA — Georgia's Supreme Court will hear arguments over an appeal filed by Ryan Duke, Tara Grinstead's accused killer, next Tuesday.

Duke's murder trial was scheduled to start April 1, but the state Supreme Court delayed that trial to hear arguments in the case.

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His lawyers want to appeal a pre-trial ruling by trial Judge Bill Reinhardt over whether the state should pay for an investigator and experts.

Reinhardt would not agree to make the state pay and also would not agree to let Duke's team appeal that decision, so Tuesday's arguments will center on whether the Supreme Court can review that pre-trial ruling.

Prosecutors argue, in effect, that Duke's team is doing an end run around the trial judge and bypassing the appeal process established under state law by the General Assembly.

Duke's lawyers argue that Reinhardt's ruling threatens his right to a fair trial.

If the court does not overturn that ruling, they say, "Mr. Duke will be forced to go to trial without the resources necessary to adequately defend himself against the state's charges."

Duke, who says he is indigent, is being represented for free by Ashleigh and John Merchant.

Prosecutors argue that, because he is not represented by a public defender, the state cannot pay for investigators and experts to help them prepare their case.

Ryan Duke is accused of murdering Grinstead, an Irwin County High School teacher, in 2005.

A second man, Bo Dukes, was convicted of helping Duke burn her body and bury it in a pecan orchard.

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The two men were charged in early 2017, more than 11 years after Tara Grinstead went missing.

Her disappearance attracted national attention and this is the second time that the Georgia Supreme Court has heard arguments in the case.

RELATED: Gag order in the Tara Grinstead murder case thrown out

A different judge imposed a gag order barring anyone associated with the case from speaking about it to the media.

13WMAZ and our Atlanta station, 11Alive, appealed that order, and last year the state Supreme Court lifted the gag order.