The case of Dr. Lishan Wang is anything but typical, right down to the debate it has stirred over whether the state should have to pay for his defense experts.

Wang is accused of fatally shooting a Yale University doctor, Vajinder Toor, outside his Branford home in 2010. Wang also allegedly fired shots at Toor's pregnant wife.

Wang had a history of confrontations with Toor at Kingsbrook Jewish Medical Center in New York where Toor once supervised Wang.

A dispute between doctors leading to murder is certainly rare. But Wang's murder case is proving to be even more peculiar as it proceeds in the criminal court system.

Wang, a Chinese citizen who was unemployed and living in Georgia before the shooting, has been deemed indigent by the court. Because of that designation, he is eligible for public defender services.

However, Wang, who remains in prison on $900,000 cash bond, wants to represent himself. And in doing so, he wants to hire expert witnesses to help his defense. Since expert witnesses do not come cheap, that request has opened the debate over who should foot the bill.

The Office of the Public Defender argues that they should not have to pay for the witnesses if Wang isn't going to use their services for his defense. (A stand-by public defender has been appointed in case Wang needs his assistance at trial or changes his mind about representing himself.)

The state Judicial Branch, who in the past has paid for services needed by a pro se defendant, also insists that it doesn't have funding in their budget for such expenditures.

An attorney appointed for Wang strictly to help sort out these pre-trial issues has asked the state Supreme Court to help resolve the dispute.

"How that specifically gets funded is neither here nor there in the eyes of the defendant," said his court-appointed private attorney, Max Simmons."Other than making the general point that a state agency is saying 'we don't have the money for this' is not a good enough answer. Someone has to find the funding for that."

Simmons, who practices law at the Law Offices of Diane Polan in New Haven, explained that Wang requested funding before Judge Patrick Clifford so that he may retain expert witnesses and an investigator to help his defense and has a constitutional right to do so.

The Office of the Public Defender was asked to provide funding for the witnesses by the judge but declined to do so. Their position is firm, if they're not doing the defense work, they shouldn't have to pay.

Then, in a rare move, Simmons was appointed to present a series of questions, called reservations, to the state Supreme Court justices. These reservations are often not answered by the state Supreme Court. The state's highest court typically waits until a case has been decided at the trial level before getting involved. Any disputes that arise in a case are then usually decided by the appellate courts on appeal.

"Trying to get [the state Supreme Court] to answer the questions is the first step," said Polan, who is not involved in the case. "Some people mistakenly think because the reservation was filed and briefed that the Supreme Court is necessarily going to answer the questions. That's not true."

The only thing that is for certain at this point is that the justices will let them know one way or another in writing. An oral argument before the state's high court is expected to be scheduled for some time in October or November.

The questions for the justices are as follows: Is an indigent defendant who qualifies for public defender services, but has waived his right to counsel, constitutionally entitled to public funds to present witnesses in order to formulate a defense?

If the answer to question one is in the affirmative, does the trial court retain the discretion to grant or deny authorization for public expenditure for any such expert witness based on the trial court's determination as to the relevance of the potential witness' testimony?

And if the answer to question one is in the affirmative, should public funds come from the state of Connecticut's Office of the Public Defender?

And lastly, if the answer to question three is in the negative, should public funds come from the Connecticut Judicial Branch?

Simmons notes in his brief that if these questions are not answered now, they'll essentially be presented on appeal, by one side or another, after the trial, regardless of the verdict.

In July, the state Public Defender's Office filed a motion to intervene in the Wang case, which Clifford denied. However, Clifford told them their input would likely be sought by the state Supreme Court if they agreed to take up the case. Both the public defenders and state Judicial Branch are expected to file amicus briefs with the state Supreme Court before the oral argument.

"By statute, the Public Defender Services Commission has the authority to promulgate policies as it deems necessary to fulfill its statutory obligations," wrote Deborah Del Prete Sullivan, legal counsel for the Chief Public Defender's Office, in their motion to Judge Clifford in July. "Acting pursuant to that authority, the Commission adopted a policy which explicitly prohibits any costs for the defense of a pro se defendant from being paid from its budget. It makes sense as the Commission is obligated to expend funds only on those clients it represents."

The brief noted that in the 2011-2012 fiscal year, the office worked on 100,945 cases and expenditures were in excess of $64 million.

The state Judicial Branch has filed an application to the state Supreme Court seeking permission to submit an amicus brief and participate in oral arguments, a move the Public Defender's Office is also expected to make.

"The answer to each of the reserved questions may have a dramatic impact on the Judicial Branch," Martin R. Libbin, director of legal services for the Branch wrote in its application.

Libbin explained that if the Supreme Court allows the trial court to provide expert witnesses to the defendant at the judge's discretion, a different judge may have to preside over that dispute because it would require the defendant to discuss their trial strategy so as to justify the expenditure.

"Certainly if the Supreme Court answers question four in the affirmative, that would have a significant impact on the expenditure of Judicial Branch funds, as the Legislature did not budget any funds to the Judicial Branch for this purpose," Libbin wrote.•