As　an　extension　of　the　spatial　autoregressive　panel　data　model　and　the　time-varying　coefficient　panel　data　model,　the　time-varying　coefficient　spatial　autoregressive　panel　data　model　is　useful　in　analysis　of　spatial　panel　data.　While　research　has　addressed　the　estimation　problem　of　this　model,　less　attention　has　been　given　to　hypotheses　tests.　This　paper　studies　two　tests　for　this　semiparametric　spatial　panel　data　model.　One　considers　the　existence　of　the　spatial　lag　term,　and　the　other　determines　whether　some　time-varying　coefficients　are　constants.　We　employ　the　profile　generalized　likelihood　ratio　test　procedure　to　construct　the　corresponding　test　statistic,　and　the　residual-based　bootstrap　procedure　is　used　to　derive　the　p-value　of　the　tests.　Some　simulations　are　conducted　to　evaluate　the　performance　of　the　proposed　test　method,　the　results　show　that　the　proposed　methods　have　good　finite　sample　properties.　Finally,　we　apply　the　proposed　test　methods　to　the　provincial　carbon　emission　data　of　China.　Our　findings　suggest　that　the　partially　linear　time-varying　coefficients　spatial　autoregressive　panel　data　model　provides　a　better　fit　for　the　carbon　emission　data.