Apply for Statehood is a decision 
Texas, as well as the releasable 
Californian Republic and 
Deseret can take. They take it to request annexation by the 
USA. These countries may take the decision if both they and the US are at peace, their relationship with the US is at least 175, and they have the same policy on slavery as the United States. The AI will always do so if possible. Taking the decision triggers the event $FROMCOUNTRY$ Applies for Statehood! for the US, who may accept or deny the application; if denied, relations between USA and the applying country will decrease by 100 and furthermore the decision can not be taken again. The AI will however always accept the application.
It is not advisable to do as the player, because the game will end from the country being annexed.
Ingame description
Our position on the North American continent, and our traditional cultural ties to the USA, make it likely that the USA would accept a petition of statehood from us. Doing this means our country will be annexed by the United States