For picklists, CRM has optionset datatype. You need to map the picklist to optionsets.
You just need to worry about the numeric value of the optionset.
Here is sample code.
OptionSetValue myOptionSet = new OptionSetValue();
myOptionSet.Value = xxxx //xxxx represents the numeric value of the option in crm.
myEntity.Attributes["optionSetAttributeName"] = myOptionSet;