Observationally derived gas-phase abundances and appropriate assumptions for the total elemental abundances of dust and gas determine the elemental composition of dust and the elemental depletion from gas in the interstellar medium (ISM). In addition to the elemental abundances, the total mass ratio of hydrogen atoms to dust grains per spatial volume is a measure of the interaction between dust and gas in the ISM. Recent remote astronomical observations and in situ measurements provide the opportunity of estimating the elemental abundances and the hydrogen gas-to-dust mass ratio of the Local Interstellar Cloud (LIC), in which the Sun is currently embedded. We show that the composition of dust in the LIC is similar to that of cometary dust in the solar system, although the nitrogen abundance remains uncertain. Depletions of elements from the LIC gas are consistent with measurements of warm neutral clouds in the Galactic disk, except for Mg and Si, which are heavily depleted in the LIC. Remote astronomical observations and in situ measurements give essentially the same value for the gas-to-dust mass ratio of the LIC, which is comparable to the average value of the diffuse ISM in the Galaxy. This indicates the association of dust with gas in the LIC, which is also inferred from the depletion pattern in the LIC. Neither the depletions of elements nor the gas-to-dust mass ratio show evidence for severe grain destruction that would result from shocks with velocity ~1.5×107 cm s-1 as suggested by a model that postulates the LIC to be a fragment of the expanding Loop I superbubble shell. Our results rather favor an alternative model that describes the origin of the LIC as being one of H I cloudlets expelled from the interaction zone between the Loop I superbubble and the Local Bubble, which encloses the LIC and similar clouds in the solar neighborhood.