The party is voting to select how candidates will be ranked for the constituency list vote next year.
Ms Davidson, who currently represents Glasgow as a list MSP, has targeted a move across the central belt to the Lothians.
Deputy leader Jackson Carlaw now heads the list for the West region.
The party attracted some criticism on social media when Ms Davidson was the only woman to feature among 20 candidates on the first lists announced. However, four more female candidates were included on the Central list announced later in the day.
Lists for the other regions will be published through the weekend.
Ms Davidson said: "This has been the most democratic system any of the parties have used to rank candidates for the regional list.
"We intend to make great progress in May, and the list vote is going to be vital for getting more Conservative MSPs into Holyrood."
Scottish Conservative leader Ruth Davidson has been selected to head her party's election list in the Lothian region.