Bootstrap procedures to calculate confidence intervals and hypotheses tests had considerable growth since its first appearance, in 1979, mostly due to the rapid computational developments that occurred in the last decades. In this work we employ the parametric and nonparametric boorstrap to study the behaviour of hyperparameters in state-space models in the case of local level and linear trend. Confidence intervals based on four different bootstrap methods are computed and compared using the coverage probabilities, with satisfactory results. We also verify the efficiency of bootstrap tests in cases where the hyperparameters lie on the boundary of the parameter space, situation that makes the classical tests inadequate to use, as it violates one of the regularity conditions of the maximum likelihood estimator.