Cross-Laminated Timber (CLT) is a renewable, sustainable, and cost-efficient building element that has been growing in popularity in recent years. To improve one of its weaknesses, suboptimal noise and vibration isolation performance, computationally efficient, accessible, and extensible CLT vibro-acoustic models are required. An effective approach for such models is the homogenisation of layered materials. This paper presents a validated homogenisation method based on First-Order Shear Deformation Theory (FSDT) that obtains the frequency-independent elastic material properties. It is applicable to arbitrary stacking sequences and orientations. The homogenised material properties are utilised with FSDT Equivalent Single Layer (ESL) models that are readily implemented with many finite element method codes to calculate the vibro-acoustic behaviour of CLT elements, even including thickness resonance effects when applied with an appropriate model. The presented homogenisation method for CLT is validated in a numerical study by comparing the mechanical mobilities of ESL models against layerwise dynamic models. The numerical study is conducted based on a validated 5-ply model, for 2- to 7-ply CLT plates with proportionally increasing thicknesses and three idealised boundary conditions. The frequency-independent material properties allow for graphical exploration of the anisotropic nature of CLT and the calculation universal anisotropic index of the considered CLT plates. The flexibility of the homogenisation method, combined with its ready implementation in already widely implemented FSDT models can have an application and impact beyond the vibro-acoustic considerations of CLT, into the general mechanical modelling of CLT as it is implemented in ever more advanced applications.