Source

File: wp-admin/includes/class-wp-upgrader.php

public function fs_connect( $directories = array(), $allow_relaxed_file_ownership = false ) {
		global $wp_filesystem;

		$credentials = $this->skin->request_filesystem_credentials( false, $directories[0], $allow_relaxed_file_ownership );
		if ( false === $credentials ) {
			return false;
		}

		if ( ! WP_Filesystem( $credentials, $directories[0], $allow_relaxed_file_ownership ) ) {
			$error = true;
			if ( is_object( $wp_filesystem ) && $wp_filesystem->errors->has_errors() ) {
				$error = $wp_filesystem->errors;
			}
			// Failed to connect. Error and request again.
			$this->skin->request_filesystem_credentials( $error, $directories[0], $allow_relaxed_file_ownership );
			return false;
		}

		if ( ! is_object( $wp_filesystem ) ) {
			return new WP_Error( 'fs_unavailable', $this->strings['fs_unavailable'] );
		}

		if ( is_wp_error( $wp_filesystem->errors ) && $wp_filesystem->errors->has_errors() ) {
			return new WP_Error( 'fs_error', $this->strings['fs_error'], $wp_filesystem->errors );
		}

		foreach ( (array) $directories as $dir ) {
			switch ( $dir ) {
				case ABSPATH:
					if ( ! $wp_filesystem->abspath() ) {
						return new WP_Error( 'fs_no_root_dir', $this->strings['fs_no_root_dir'] );
					}
					break;
				case WP_CONTENT_DIR:
					if ( ! $wp_filesystem->wp_content_dir() ) {
						return new WP_Error( 'fs_no_content_dir', $this->strings['fs_no_content_dir'] );
					}
					break;
				case WP_PLUGIN_DIR:
					if ( ! $wp_filesystem->wp_plugins_dir() ) {
						return new WP_Error( 'fs_no_plugins_dir', $this->strings['fs_no_plugins_dir'] );
					}
					break;
				case get_theme_root():
					if ( ! $wp_filesystem->wp_themes_dir() ) {
						return new WP_Error( 'fs_no_themes_dir', $this->strings['fs_no_themes_dir'] );
					}
					break;
				default:
					if ( ! $wp_filesystem->find_folder( $dir ) ) {
						return new WP_Error( 'fs_no_folder', sprintf( $this->strings['fs_no_folder'], esc_html( basename( $dir ) ) ) );
					}
					break;
			}
		}
		return true;
	}