1. A speech recognition apparatus comprising: a first recognition dictionary that stores a plurality of first phoneme strings, which are respectively converted from a plurality of text data; a speech input unit that inputs a speech made by a user; a speech recognition unit that recognizes the speech based on the first recognition dictionary and outputs a first recognition result; a speech transmission unit that transmits the speech to a server, the server including a second recognition dictionary that stores a plurality of second phoneme strings respectively converted from the plurality of text data, the server recognizing the speech based on the second recognition dictionary and outputting a second recognition result; a recognition result receipt unit that receives the second recognition result from the server; and a control unit that determines a likelihood level of a selected candidate obtained based on the first recognition result, and controls an output unit to output at least one of the first recognition result and the second recognition result based on a determination result of the likelihood level of the selected candidate, wherein, when the likelihood level of the selected candidate is equal to or higher than a threshold level, the control unit controls the output unit to output the first recognition result irrespective of whether the recognition result receipt unit receives the second recognition result from the server.