By means of numerical experiments, the influence of the value of the asteroid’s own rotational velocity, orientation of the axis of rotation, and figure parameters on the magnitude of perturbations in its rotational dynamics arising during close approach to the Earth is studied. Two cases are considered: 1) asteroid (99942) Apophis with a relatively slow rotation (period ≈ 30 h) and 2) asteroid 2012 TC4, which has a fast rotation (period ≈ 12 min). It was found that in the case of asteroids with slow rotation, perturbations can be large: in the case of Apophis, when approaching the Earth in 2029, changes in the rotational period ∆P may reach tens of hours, and deviations in the orientation of the axis of rotation ∆γ — tens of degrees. For fast-rotating asteroids, the perturbations are very small: in the case of asteroid 2012 TC4 at its approach to the Earth in 2017, |∆P | < 10−5 min, |∆γ| < 0.01◦. It is shown that for asteroids with slow rotation, the uncertainty in the determination of asteroid figure parameters (moments of inertia) can lead to noticeable inaccuracies in the estimation of perturbation magnitudes. The uncertainty in the knowledge of the figure parameters of a fast-rotating asteroid practically does not affect the estimation of perturbations in its rotational dynamics. In the case of Apophis, changes in the rotational velocity and orientation of the axis of rotation during the upcoming 2029 approach to the Earth may lead to a decrease in the value of the parameter A2, which characterizes the Yarkovsky effect, to −1.5 · 10−14 a.u./d2, or to an increase up to −3.5 · 10−14 a.u./d2. Perturbations in the rotational dynamics of asteroid 2012 TC4 during its approach to the Earth in 2017 did not affect the value of parameter A2.