Sept 7 (Reuters) - Israeli police recommended on Sunday that criminal charges be filed against Prime Minister Ehud Olmert, who has vowed to resign this month amid a series of scandals.

Israel's attorney-general has the final word on whether to indict Olmert, a process that could be protracted.

Following are three scenarios for what might happen next in Israel's shaken political system:

* Israeli opinion polls show Foreign Minister Tzipi Livni and Transport Minister Shaul Mofaz, a former defence chief, are favourites to win a Sept. 17 election to succeed Olmert as Kadima party leader. Either could forge a coalition similar to the current one. It would take office once sworn in by parliament in late October. Olmert would remain caretaker prime minister until then.

* Some of Olmert's bickering coalition partners might balk at joining a coalition with the more politically moderate Livni if she becomes Kadima leader. These parties could swing behind rightist parliamentary opposition leader Benjamin Netanyahu, and force President Shimon Peres to ask Netanyahu to try to form a coalition. Such a government might be reluctant to pursue U.S.-backed peace talks with the Palestinians or indirect negotiations with Syria.

* Olmert's resignation could prompt a majority in parliament to opt for an early election. Parliament could dissolve itself and set an election date before the scheduled date of 2010.

An election must be held within five months of the Knesset voting to dissolve itself, but the gap is usually shorter. Recent opinion polls show Netanyahu's Likud party would emerge strongest if a vote were held now. Such a scenario could leave Olmert as caretaker prime minister until a government is formed after the election.

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