For potential applications in ferroelectric switching and piezoelectric nano-generator devices, the promising ferroelectric properties of two dimensional (2D) layered In2Se3 attracted much attention. In the present study, 2D In2Se3 flakes down to monolayers are grown by the chemical vapor deposition (CVD) technique on a mica substrate with their structural, optical and ferroelectric properties being studied. The effect of growth parameters (time of growth and Ar flow rate) on the shape and size of the deposited flakes was studied. The optical microscopy study revealed that the flake changed from a circular shape to a sharp face triangle as the Ar flow rate and growth time increased. Raman spectroscopy and high-resolution scanning transmission electron microscopy (HR-STEM) studies revealed that the flakes were of α and β phases, each of which has a hexagonal crystal structure. Strong second harmonic generation (SHG) was observed from α-In2Se3, demonstrating its non-centrosymmetric structure. The piezo-force microscopic (PFM) study showed the presence of out of plane (OOP) ferroelectricity with no in plane (IP) ferroelectricity in CVD grown α-In2Se3 indicating its vertically confined piezoresponse, which was tuned by the applied electric bias and the flake thickness. The present result of shape-controlled growth of In2Se3 with OOP ferroelectricity would open new pathways in the field of 2D ferroelectric switching devices.