Alzheimer's disease manifests with both cognitive and motor deficits. However, the degree to which genetic risk of Alzheimer's dementia contributes to late-life motor impairment, and the specific molecular systems underlying these associations, are uncertain. Here, we adopted an integrative multi-omic approach to assess genetic influence on motor impairment in older adults and identified key molecular pathways that may mediate this risk. We built a polygenic risk score for clinical diagnosis of Alzheimer's dementia (AD-PRS) and examined its relationship to several motor phenotypes in 1885 older individuals from two longitudinal aging cohorts. We found that AD-PRS was associated with a previously validated composite motor scores and their components. The major genetic risk factor for sporadic Alzheimer's dementia, the APOE/TOMM40 locus, was not a major driver of these associations. To identify specific molecular features that potentially medicate the genetic risk into motor dysfunction, we examined brain multi-omics, including transcriptome, DNA methylation, histone acetylation (H3K9AC), and targeted proteomics, as well as diverse neuropathologies. We found that a small number of factors account for the majority of the influence of AD-PRS on motor function, which comprises paired helical filament tau-tangle density, H3K9AC in specific chromosomal regions encoding genes involved in neuromuscular process. These multi-omic factors have the potential to elucidate key molecular mechanisms developing motor impairment in the context of Alzheimer's dementia.