Superconducting gap structure was probed in type-II Dirac semimetal PdTe2 by measuring the London penetration depth using the tunnel diode resonator technique. At low temperatures, the data for two samples are well described by a weak-coupling exponential fit yielding λ(T=0)=230 nm as the only fit parameter at a fixed Δ(0)/Tc≈1.76, and the calculated superfluid density is consistent with a fully gapped superconducting state characterized by a single gap scale. Electrical resistivity measurements for in-plane and inter-plane current directions find very low and nearly temperature-independent normal-state anisotropy. The temperature dependence of resistivity is typical for conventional phonon scattering in metals. We compare these experimental results with expectations from a detailed theoretical symmetry analysis and reduce the number of possible superconducting pairing states in PdTe2 to only three nodeless candidates: a regular, topologically trivial s-wave pairing, and two distinct odd-parity triplet states that both can be topologically nontrivial depending on the microscopic interactions driving the superconducting instability.