In this paper we evaluate the local seismic response for thirteen sites located in the municipalities of Arquata del Tronto and Montegallo, two areas which suffered heavy damage during the Mw 6.0 and Mw 5.4 earthquakes which struck Central Italy on August 24, 2016. The input dataset is made by ground motion recordings of 348 events occurred during the sequence. The spectral site response is estimated by the Generalized Inversion Technique and makes use of reference sites. The interpretation is further improved through the information provided by a reference-site independent method (i.e., the so called Receiver-Function Technique) and by the Horizontal-to-Vertical Spectral Ratios of ambient noise recordings. We also provide an independent estimate of the local amplification by comparing the Peak Ground Velocity and the Spectral Amplitudes observed at each site to the value estimated by well-established Ground Motion Prediction Equations for a rock-class site. The results obtained by the adopted methodologies are all highly consistent, and they emphasize the different seismic behavior of several sites at local scale. Thus, sites located on Quaternary deposits overlying the bedrock, such as Castro, Pretare, Spelonga, Pescara del Tronto, and Capodacqua feature some relevant amplifications in a medium (2-10 Hz) frequency range; two sites at Spelonga show amplifications also at low frequencies; three sites located on stiff formations, i.e. Uscerno, Balzo and Colle d'Arquata, respectively, feature either nearly neutral response or low amplification level. A probable topographic effect was identified at the rock site of Rocca di Arquata (MZ80).