1. A speech recognition apparatus comprising: a local database storing a plurality of local text data; a text data obtaining unit that obtains a plurality of subject text data from an external device; a text data transmission unit that transmits the plurality of subject text data to a server; a first recognition dictionary that stores a plurality of first phoneme strings, which are respectively converted from the plurality of subject text data; a recognition dictionary preparation unit that prepares the first recognition dictionary by: respectively converting the plurality of subject text data to the plurality of first phoneme strings when each of the plurality of subject text data is equal to one of the plurality of local text data stored in the local database, and storing the plurality of first phoneme strings in the first recognition dictionary; a speech input unit that inputs a speech made by a user; a speech recognition unit that recognizes the speech by referring to the first recognition dictionary and outputs a first recognition result; a speech transmission unit that transmits the speech to the server, which includes a second recognition dictionary that stores a plurality of second phoneme strings respectively converted from the plurality of subject text data, the server recognizing the speech by referring to 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 or the second recognition result based on a determination result of the likelihood level of the selected candidate, wherein the server includes a server database storing a plurality of server text data, an amount of the server text data stored in the server database being larger than an amount of the local text data stored in the local database; wherein the server: converts each of the subject text data received from the text data transmission unit to one of the plurality of second phoneme strings when each of the subject text data is equal to one of the plurality of server text data stored in the server database, and stores the plurality of second phoneme strings in the second recognition dictionary; and 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.