I have a real data set ($n=50$). I would like to fit some parametric models to this data set and then compare the maximum log-likelihood values with my spline model which is a nonparametric model. Could I use AIC criteria as a model selection? If not, which model selection criteria can I use?
You shouldn't generally use AIC to choose between parametric and nonparametric models. Parametric and nonparametric models have different modeling assumptions. The traditional AIC is based on a function of the likelihood. Likelihoods of parametric and nonparametric models are not always comparable.
An alternative that in theory can naturally compare parametric and nonparametric is a generalized degrees of freedom based criteria. See Ye's paper or Huang and Chen's paper for geostatistical data