Is the circuit a Parallel RLC if there is a voltage source in between capacitor and inductor?
In comments, you say you'll apply a stimulus at the location of V1. In that case, you can redraw the circuit like this:







simulate this circuit &ndash; Schematic created using CircuitLab

You can see that as far as this stimulus is concerned, the L and C elements are not in parallel. Nor are they strictly in series, since not all current through the C element also flows through the L element. 

You can also see immediately that this circuit has some behavior that doesn't match either a parallel or series RLC circuit. For example, the impedance goes to inifinity (like a series RLC circuit) at \$\omega=0\$, but it goes to R (instead of to infinity again) in the limit as \$\omega\to\infty\$.

Short answer: This circuit does not behave like either a series or parallel RLC circuit.