  Silicon spin qubits show great promise as a scalable qubit platform for
fault-tolerant quantum computing. However, fast high-fidelity readout of charge
and spin states, which is required for quantum error correction, has remained
elusive. Radio-frequency reflectometry enables rapid high-fidelity readout of
GaAs spin qubits, but the relatively large resistances and capacitances of
accumulation-mode Si quantum dot devices have made radio-frequency
reflectometry challenging in these platforms. In this work, we implement
radio-frequency reflectometry in a Si/SiGe quantum dot device with overlapping
gates by making minor device-level changes that eliminate these challenges. We
demonstrate charge state readout with a fidelity above 99.9% in an integration
time of 300 ns. We measure the singlet and triplet states of a double quantum
dot via both conventional Pauli spin blockade and a charge latching mechanism,
and we achieve maximum fidelities of 82.9% and 99.0% in 2.08 $\mu$s and 1.6
$\mu$s integration times, respectively. We also use radio-frequency
reflectometry to perform single-shot readout of single-spin states via
spin-selective tunneling in microsecond-scale integration times.
