"To request a recount" means asking for another count or tally of something, usually votes in an election, to ensure accuracy or challenge the initial result. Full definition
On Sunday afternoon, Democratic Assemblyman John A. Perez, who finished just 481 votes behind Board of Equalization member Betty Yee in the June 3rd primary, formally requested a recount in the controller's race. (calnewsroom.com)
4 - Any candidate who disputes the result, can then request a recount - though an «unreasonable» request may be refused by the Returning Officer. (politics.stackexchange.com)
In that race, Democratic challenger Tom Perriello was certified the winner over incumbent Republican Rep. Virgil Goode, but the margin - less than 800 votes - was close enough for Goode to request a recount under state law. (politicalticker.blogs.cnn.com)