Local Road Safety Act of 2014 - Revises requirements for a state strategic highway safety plan.

Requires a state transportation department to develop a plan after consultation with, among other things, private sector experts in the field of roadway safety infrastructure. Requires the department, in developing such plan, also to consider, among other things, the results of any strategic highway safety plan developed by a county or local government entity or regional transportation planning organization.

Prescribes a special rule requiring states to provide each fiscal year, from their apportionment of highway safety improvement program funds, an amount to county and local transportation agencies necessary to assist them to address significant safety needs, and high fatality segments, of non-state-owned public roads and roads on tribal lands identified in a state strategic highway safety plan.