President Katsav claimed he had received blackmail threats, while his former secretary claims she was sexually harassed by him.
The police's top brass has in the meantime been "sitting on the fence" and waiting to see whether the ball reaches their court.
A senior police source said that "the procedure is that when a police complaint arrives, we launch an investigation, but if enough evidence is collected by the attorney general, he can also order an investigation, and we can launch it without a complaint."
The same source added: "The police do not expect such an incident. And it could be that in the end the attorney general will decide that there is enough evidence and no complaints have been launched. In such a case, no investigation will be launched."
Another senior source in the police said: "Although in theory this is a relatively simple investigation of collecting witness statements by both sides, due to the sensitivity and the status of the sides involved, the investigation is complicated."
'A fashionable trend'
Another source said that "even if the complaint is lodged in Jerusalem or in a different district, because of its importance and sensitivity it will be directly transferred to a national police unit, and would not be treated regionally."
Eliad Shraga, a lawyer who heads the Movement for Quality of Government in Israel, told Ynet: "The fashionable trend is now to lodge complaints with the media rather than the police, due to the fact that the attorney general agrees to live with such norms."
"One of two situations should be taking place – either there is a real complaint and then a letter should be submitted to the attorney general, who will then decide if it is right to launch an investigation or whether the claim is unsubstantiated. In such a case, all of those lodging a complaint must be tried, and the punishment for false accusations is three years in prison," he said.
The Movement for Quality of Government said it wondered why the number one citizen in Israel was complaining that someone was attempting to blackmail him for money.
"It's unacceptable that the president is being threatened and the attorney general agrees with him when he says that this is not a criminal incident," added Shraga.
Aviram Zino contributed to the report