  Measurement-based quantum error correction relies on the ability to determine
the state of a subset of qubits (ancillae) within a processor without revealing
or disturbing the state of the remaining qubits. Among neutral-atom based
platforms, a scalable, high-fidelity approach to mid-circuit measurement that
retains the ancilla qubits in a state suitable for future operations has not
yet been demonstrated. In this work, we perform imaging using a
narrow-linewidth transition in an array of tweezer-confined $^{171}$Yb atoms to
demonstrate nondestructive state-selective and site-selective detection. By
applying site-specific light shifts, selected atoms within the array can be
hidden from imaging light, which allows a subset of qubits to be measured while
causing only percent-level errors on the remaining qubits. As a
proof-of-principle demonstration of conditional operations based on the results
of the mid-circuit measurements, and of our ability to reuse ancilla qubits, we
perform conditional refilling of ancilla sites to correct for occasional atom
loss, while maintaining the coherence of data qubits. Looking towards true
continuous operation, we demonstrate loading of a magneto-optical trap with a
minimal degree of qubit decoherence.
